BOUNDEDNESS OF DYADIC DERIVATIVE AND CESARO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES
In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα （0 α ∞）, respectively. The facts show that it depends on the geometrical...
Saved in:
| Published in | Acta mathematica scientia Vol. 31; no. 1; pp. 268 - 280 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
2011
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(11)60227-0 |
Cover
| Abstract | In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα （0 α ∞）, respectively. The facts show that it depends on the geometrical properties of the Banach space. |
|---|---|
| AbstractList | In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I
* and Cesàro mean operator σ
* are bounded from the B-valued martingale Hardy spaces
▪ to
Lα (0 < α < ∞), respectively. The facts show that it depends on the geometrical properties of the Banach space. In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα （0 α ∞）, respectively. The facts show that it depends on the geometrical properties of the Banach space. |
| Author | 陈丽红 刘培德 |
| AuthorAffiliation | College of Science, Wuhan Textile University, Wuhan 430073, China School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
| Author_xml | – sequence: 1 fullname: 陈丽红 刘培德 |
| BookMark | eNqFkEtLw0AUhQepYFv9CcLgShfRmUkm06xk2kxroE1K0hYEYcjjpkZrqkkR_PdOH7h1cw9czncfp4c69bYGhK4puaeEug8JYZxZnkvYLaV3RpiwyBnqUi5MmwxEB3X_LBeo17ZvxHDMdbroZRgtQ1_5oUoSHI2x_yz9YIR9FQcruQhWCsvQxyOVyDjCMyVDHM1VLBdRjKMQJ9FM4aG1ktOl8vFMxosgnMipwslcGuYSnZfppoWrk_bRcqwWoydrGk2CkZxaORs4O0sUpcjcjHkEXI8DMIdzKhygrgBemsJSXpaQesYNvCCpPcgLcIWd5SktWGH3ET_OzZtt2zZQ6s-m-kibH02J3kekDxHp_f-aUn2ISBPDPR45MMd9V9DoNq-gzqGoGsh3uthW_064OW1-3dbrr6pe6yzN38tqA9p2uW1zR9i_M45y0w |
| Cites_doi | 10.1007/BF02771074 10.1007/BF01197890 10.1080/00036819608840480 10.1007/BF02205221 10.1090/S0002-9947-1949-0032833-2 10.1007/s10114-005-0627-0 10.1080/00036818908839895 10.4064/sm-120-3-271-288 10.1080/00036817308839055 |
| ContentType | Journal Article |
| Copyright | 2011 Wuhan Institute of Physics and Mathematics |
| Copyright_xml | – notice: 2011 Wuhan Institute of Physics and Mathematics |
| DBID | 2RA 92L CQIGP W94 ~WA AAYXX CITATION |
| DOI | 10.1016/S0252-9602(11)60227-0 |
| DatabaseName | 维普_期刊 中文科技期刊数据库-CALIS站点 中文科技期刊数据库-7.0平台 中文科技期刊数据库-自然科学 中文科技期刊数据库- 镜像站点 CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics Physics |
| DocumentTitleAlternate | BOUNDEDNESS OF DYADIC DERIVATIVE AND CESARO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES |
| EISSN | 1572-9087 |
| EndPage | 280 |
| ExternalDocumentID | 10_1016_S0252_9602_11_60227_0 S0252960211602270 36533547 |
| GrantInformation_xml | – fundername: Wuhan University of Science and Engineering grantid: 093877 – fundername: the Nation Natural Science Foundation of China grantid: 10671147 |
| GroupedDBID | --K --M -01 -0A -EM -SA -S~ .~1 0R~ 1B1 1~. 1~5 23M 2B. 2C. 2RA 4.4 406 457 4G. 5GY 5VR 5VS 5XA 5XB 5XL 7-5 71M 8P~ 92E 92I 92L 92M 92Q 93N 9D9 9DA AACTN AAEDT AAFGU AAHNG AAIKJ AAKOC AALMO AALRI AAOAW AAPBV AAQFI AAUYE AAXUO ABAOU ABECU ABFGW ABFNM ABFTV ABKAS ABKCH ABMAC ABMQK ABPIF ABTEG ABTMW ABXDB ABXPI ABYKQ ACAZW ACBMV ACBRV ACBYP ACDAQ ACGFS ACHSB ACIGE ACIPQ ACMLO ACRLP ACTTH ACVWB ACWMK ADALY ADBBV ADEZE ADKNI ADMDM ADTIX ADURQ ADYFF AEBSH AEFTE AEJRE AEKER AENEX AESTI AEVTX AFKWA AFQWF AFUIB AGDGC AGGBP AGHFR AGJBK AGMZJ AGUBO AGYEJ AIAKS AIEXJ AIGVJ AIKHN AILAN AIMYW AITGF AITUG AJBFU AJDOV AJOXV AJZVZ AKQUC ALMA_UNASSIGNED_HOLDINGS AMFUW AMKLP AMRAJ AMYLF ARUGR AXJTR AXYYD BGNMA BKOJK BLXMC CAJEA CAJUS CCEZO CCVFK CDYEO CHBEP CIAHI CQIGP CS3 CSCUP CW9 EBLON EBS EFJIC EJD EO9 EP2 EP3 FA0 FDB FEDTE FIRID FNLPD FNPLU FYGXN GBLVA GJIRD HVGLF HZ~ IPNFZ J1W JUIAU JZLTJ KOM KOV LLZTM M41 M4Y MHUIS MO0 N9A NQJWS NU0 O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q-- Q-0 Q38 R-A REI RIG ROL RSV RT1 S.. SDC SDF SDG SDH SES SNE SOJ SPC SRMVM SSLCW SSW SSZ T5K T8Q TCJ TGP TSG U1F U1G U5A U5K UOJIU UTJUX VFIZW W94 ZMTXR ~G- ~L9 ~WA AAEDW AATNV AAYFA ABTKH ACOKC ACZOJ ADMUD ADOXG ADTPH AESKC AFNRJ AGQEE AMXSW DPUIP EFLBG FIGPU IKXTQ IWAJR NPVJJ PT4 SNPRN SOHCF VEKWB AACDK AAJBT AASML AATTM AAXKI AAYWO AAYXX ABAKF ABBRH ABDBE ABFSG ABJNI ABWVN ACAOD ACDTI ACPIV ACRPL ACSTC ACVFH ADCNI ADNMO AEFQL AEIPS AEMSY AEUPX AEZWR AFBBN AFDZB AFHIU AFOHR AFPUW AFXIZ AGCQF AGRNS AHPBZ AHWEU AIGII AIGIU AIIUN AIXLP AKBMS AKRWK AKYEP ANKPU ATHPR AYFIA CITATION HG6 SJYHP SSH |
| ID | FETCH-LOGICAL-c284t-7df7b6b290e695ee2455174e167e5f67e2a5ffea9284e5d0a38cde673bca1d2d3 |
| IEDL.DBID | AIKHN |
| ISSN | 0252-9602 |
| IngestDate | Tue Jul 01 02:27:31 EDT 2025 Fri Feb 23 02:25:03 EST 2024 Thu Nov 24 20:27:52 EST 2022 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | martingale space dyadic integral dyadic derivative 60G42 43A17 B-valued martingale |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c284t-7df7b6b290e695ee2455174e167e5f67e2a5ffea9284e5d0a38cde673bca1d2d3 |
| Notes | martingale space dyadic derivative B-valued martingale O174.41 dyadic integral 42-1227/O B-valued martingale; martingale space; dyadic derivative; dyadic integral O177.2 |
| PageCount | 13 |
| ParticipantIDs | crossref_primary_10_1016_S0252_9602_11_60227_0 elsevier_sciencedirect_doi_10_1016_S0252_9602_11_60227_0 chongqing_backfile_36533547 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2011 2011-1-00 |
| PublicationDateYYYYMMDD | 2011-01-01 |
| PublicationDate_xml | – year: 2011 text: 2011 |
| PublicationDecade | 2010 |
| PublicationTitle | Acta mathematica scientia |
| PublicationTitleAlternate | Acta Mathematica Scientia |
| PublicationYear | 2011 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Weisz (bib8) 1996; 22 Weisz (bib7) 1996; 62 Liu, Yu (bib14) 2001; 31 Nie, Li, Lou (bib11) 2005; 21 Butzer, Wagner (bib1) 1973; 3 Schipp, Wade (bib4) 1989; 34 Weisz (bib5) 1998; 24 Weisz (bib10) 1990; 84 Weisz (bib6) 1996; 120 Liu, Hou (bib13) 1998; 28 Schipp, Wade, Simon, Pál (bib2) 1990 Schipp (bib3) 1974; 4 Liu (bib12) 1993 Long (bib16) 1993 Fine (bib15) 1949; 65 Weisz (bib9) 1994 Weisz (10.1016/S0252-9602(11)60227-0_bib10) 1990; 84 Weisz (10.1016/S0252-9602(11)60227-0_bib9) 1994 Weisz (10.1016/S0252-9602(11)60227-0_bib5) 1998; 24 Weisz (10.1016/S0252-9602(11)60227-0_bib6) 1996; 120 Schipp (10.1016/S0252-9602(11)60227-0_bib2) 1990 Schipp (10.1016/S0252-9602(11)60227-0_bib4) 1989; 34 Long (10.1016/S0252-9602(11)60227-0_bib16) 1993 Fine (10.1016/S0252-9602(11)60227-0_bib15) 1949; 65 Weisz (10.1016/S0252-9602(11)60227-0_bib8) 1996; 22 Liu (10.1016/S0252-9602(11)60227-0_bib14) 2001; 31 Liu (10.1016/S0252-9602(11)60227-0_bib13) 1998; 28 Nie (10.1016/S0252-9602(11)60227-0_bib11) 2005; 21 Liu (10.1016/S0252-9602(11)60227-0_bib12) 1993 Weisz (10.1016/S0252-9602(11)60227-0_bib7) 1996; 62 Schipp (10.1016/S0252-9602(11)60227-0_bib3) 1974; 4 Butzer (10.1016/S0252-9602(11)60227-0_bib1) 1973; 3 |
| References_xml | – volume: 22 start-page: 229 year: 1996 end-page: 242 ident: bib8 article-title: Cesàro summability of one- and two-dimensional Walsh-Fourier series publication-title: Analysis Math – volume: 31 start-page: 615 year: 2001 end-page: 625 ident: bib14 article-title: B-valued small index martingale space and atom decompositions publication-title: Science in China – volume: 84 start-page: 361 year: 1990 end-page: 376 ident: bib10 article-title: Martingale Hardy spaces for 0< publication-title: Probab Th Rel Fields – year: 1990 ident: bib2 publication-title: Walsh series: An introduction to dyadic harmonic analysis – volume: 3 start-page: 29 year: 1973 end-page: 46 ident: bib1 article-title: Walsh series and the concept of a derivative publication-title: Appl Anal – volume: 34 start-page: 203 year: 1989 end-page: 218 ident: bib4 article-title: A fundamental theorem of dyadic calculus for the unit square publication-title: Appl Anal – volume: 21 start-page: 1465 year: 2005 end-page: 1474 ident: bib11 article-title: The martingale Hardy type inequalities for dyadic derivative and integral publication-title: Acta Mathematica Sinica, English series – volume: 65 start-page: 372 year: 1949 end-page: 414 ident: bib15 article-title: On the Walsh functions publication-title: Trans Amer Math Soc – year: 1993 ident: bib16 publication-title: Martingale spaces and inequalities – volume: 28 start-page: 884 year: 1998 end-page: 892 ident: bib13 article-title: Atomic decompositions of Banach-space-valued martingales publication-title: Science in China, Series A – year: 1994 ident: bib9 publication-title: Martingale Hardy spaces and their applications in Fourier-analysis, volume 1568 of Lecture Notes in Math – year: 1993 ident: bib12 publication-title: Martingales and geometry in Banach spaces – volume: 120 start-page: 271 year: 1996 end-page: 288 ident: bib6 article-title: ( publication-title: Studia Math – volume: 24 start-page: 59 year: 1998 end-page: 77 ident: bib5 article-title: Martingale Hardy spaces and the dyadic derivative publication-title: Analysis Math – volume: 4 start-page: 541 year: 1974 end-page: 546 ident: bib3 article-title: Übereinen Ableitung sbegriff von P.L.Butzer and H.J. Wagner publication-title: Mat Balkanica – volume: 62 start-page: 223 year: 1996 end-page: 238 ident: bib7 article-title: Some maximal inequalities with respect to two-parameter dyadic derivative and Cesàro summability publication-title: Applic Anal – volume: 24 start-page: 59 year: 1998 ident: 10.1016/S0252-9602(11)60227-0_bib5 article-title: Martingale Hardy spaces and the dyadic derivative publication-title: Analysis Math doi: 10.1007/BF02771074 – year: 1993 ident: 10.1016/S0252-9602(11)60227-0_bib16 – volume: 84 start-page: 361 year: 1990 ident: 10.1016/S0252-9602(11)60227-0_bib10 article-title: Martingale Hardy spaces for 0<p≤1 publication-title: Probab Th Rel Fields doi: 10.1007/BF01197890 – volume: 62 start-page: 223 year: 1996 ident: 10.1016/S0252-9602(11)60227-0_bib7 article-title: Some maximal inequalities with respect to two-parameter dyadic derivative and Cesàro summability publication-title: Applic Anal doi: 10.1080/00036819608840480 – volume: 22 start-page: 229 year: 1996 ident: 10.1016/S0252-9602(11)60227-0_bib8 article-title: Cesàro summability of one- and two-dimensional Walsh-Fourier series publication-title: Analysis Math doi: 10.1007/BF02205221 – volume: 65 start-page: 372 year: 1949 ident: 10.1016/S0252-9602(11)60227-0_bib15 article-title: On the Walsh functions publication-title: Trans Amer Math Soc doi: 10.1090/S0002-9947-1949-0032833-2 – year: 1990 ident: 10.1016/S0252-9602(11)60227-0_bib2 – volume: 4 start-page: 541 year: 1974 ident: 10.1016/S0252-9602(11)60227-0_bib3 article-title: Übereinen Ableitung sbegriff von P.L.Butzer and H.J. Wagner publication-title: Mat Balkanica – volume: 21 start-page: 1465 issue: 6 year: 2005 ident: 10.1016/S0252-9602(11)60227-0_bib11 article-title: The martingale Hardy type inequalities for dyadic derivative and integral publication-title: Acta Mathematica Sinica, English series doi: 10.1007/s10114-005-0627-0 – volume: 31 start-page: 615 issue: 7 year: 2001 ident: 10.1016/S0252-9602(11)60227-0_bib14 article-title: B-valued small index martingale space and atom decompositions publication-title: Science in China – volume: 34 start-page: 203 year: 1989 ident: 10.1016/S0252-9602(11)60227-0_bib4 article-title: A fundamental theorem of dyadic calculus for the unit square publication-title: Appl Anal doi: 10.1080/00036818908839895 – year: 1994 ident: 10.1016/S0252-9602(11)60227-0_bib9 – volume: 28 start-page: 884 issue: 10 year: 1998 ident: 10.1016/S0252-9602(11)60227-0_bib13 article-title: Atomic decompositions of Banach-space-valued martingales publication-title: Science in China, Series A – volume: 120 start-page: 271 year: 1996 ident: 10.1016/S0252-9602(11)60227-0_bib6 article-title: (Hp,Lp)-type inequalities for the two-dimensional dyadic derivative publication-title: Studia Math doi: 10.4064/sm-120-3-271-288 – volume: 3 start-page: 29 year: 1973 ident: 10.1016/S0252-9602(11)60227-0_bib1 article-title: Walsh series and the concept of a derivative publication-title: Appl Anal doi: 10.1080/00036817308839055 – year: 1993 ident: 10.1016/S0252-9602(11)60227-0_bib12 |
| SSID | ssj0016264 |
| Score | 1.8115678 |
| Snippet | In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from... In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I * and Cesàro mean operator σ * are bounded... |
| SourceID | crossref elsevier chongqing |
| SourceType | Index Database Publisher |
| StartPage | 268 |
| SubjectTerms | 43A17 60G42 B-valued martingale Banach空间 B值鞅空间 CES dyadic derivative dyadic integral martingale space 二进导数 几何性质 平均算子 有界性 鞅Hardy空间 |
| Title | BOUNDEDNESS OF DYADIC DERIVATIVE AND CESARO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES |
| URI | http://lib.cqvip.com/qk/86464X/20111/36533547.html https://dx.doi.org/10.1016/S0252-9602(11)60227-0 |
| Volume | 31 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PT9swFH5iRZO2w2BsiA5W-bADO7jNLzvNsVRUham9jEpcpsixX6BCTbq2m8SF_4W_hX-MZyctm4Q4IEWRYvlH5Oe873ux_RngW54lMcZGch-V4uT9NCecMVxnRLa7BOmR218xGsvhJDq_FJdb0F_vhbHLKmvfX_l0563rlE7dm535dNr5SWgdEP-mCEZaHTyK27eDMJGiAdu9sx_D8WYygTi7U5Gi_NwWeNrIU1XiEo99_7urh3tWZuG6LK5-E3g8D1f_QNBgFz7U3JH1qtf7CFtY7MFOzSNZ_ZUu9-D9aKPFSk9v3SJPvfwEv07sGUporHdjZc7MrTJTzQwNwr9O_5upwrA-Lh_uFyWboSpYOUc3D8_Kgi3LGbITbuXBqbmZ0x-w-MLIKVG7n2EyOL3oD3l9vALXhEkrHps8zmQWJB7KRCAGkbCy1ejLGEVOt0CJPEeVUG4UxlNhVxuUcZhp5ZvAhPvQKMoCD4BJHz2kYEbkSkVRmHV1QGGMDjHytBdp3YTDTY8SPOsbKzqVhpK4pojiJrTXfZzOK42N9GnxGRkotQaiWCV1Bkq9JnTXlkj_Gywp4cDLRb-8vughvKt-KNvrCBqrxR_8SoxklbXgTfvOb9Xj7hG1BNqh |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwEB4hEGp74NWiLq_6wIEezOZhO7tHWIEWynIBJC6V5diTdoU22bJbJC78l_6W_jHGTnZpJdRDpShSLDuOPM583yTjzwD7Rd7NMHOKx2gMJ-9nOeGM4zYnst0hSBdhfcXgUvVvxPmtvF2A3mwtjE-rbHx_7dODt25K2s1otsfDYfuK0Doh_k0RjPI6eBS3LwmZZj6v7_BpnucRE2MPGlJUm_vqL8t46luEwoM4_hzuwiMvsvC9Kr_9IOh4Haz-AKDTNVhpmCM7qh9uHRaw3IDVhkWy5h2dbMC7wVyJla6WQ4qnnbyHr8d-ByV03rexqmDu0bihZY6m4ENQ_2amdKyHk9-_7is2QlOyaozhLzyrSjapRsiOuRcHp-5GQX3Aowsjl0T9foCb05PrXp83mytwS4g05ZkrslzlSTdC1ZWIiZBetBpjlaEs6JQYWRRoulQbpYtM2rEOVZbm1sQucekmLJZViR-BqRgjpFBGFsYIkeYdm1AQY1MUkY2EtS3Yno8ogbO985JTOlXENKXIWnA4G2M9rhU29EvqGRlIewNRpKKDgXTUgs7MEvqvqaIJBf7ddOv_m36CN_3rwYW-OLv8sg1v60_L_tiBxen9T9wlbjLN98LcewaCtdts |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Boundedness+of+dyadic+derivative+and+Ces%C3%A1ro+mean+operator+on+some+B-valued+martingale+spaces&rft.jtitle=Acta+mathematica+scientia&rft.au=Lihong%2C+Chen&rft.au=Peide%2C+Liu&rft.date=2011&rft.pub=Elsevier+Ltd&rft.issn=0252-9602&rft.eissn=1572-9087&rft.volume=31&rft.issue=1&rft.spage=268&rft.epage=280&rft_id=info:doi/10.1016%2FS0252-9602%2811%2960227-0&rft.externalDocID=S0252960211602270 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fimage.cqvip.com%2Fvip1000%2Fqk%2F86464X%2F86464X.jpg |