An L p version of Hardy's theorem for the Jacobi-Dunkl transform
In this paper, we give a generalization of Hardy's theorem for the Jacobi-Dunkl transform ℱ on ℝ. More precisely for all a > 0, b > 0 and p, q ∈ [1, +∞], we determine the measurable functions f on ℝ such that E 1/4a −1 f ∈ L α,β p (ℝ) and e bλ 2 ℱf ∈ L σ q (ℝ), where E t , t > 0, L α,β...
Saved in:
| Published in | Integral transforms and special functions Vol. 15; no. 3; pp. 225 - 237 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.06.2004
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this paper, we give a generalization of Hardy's theorem for the Jacobi-Dunkl transform ℱ on ℝ. More precisely for all a > 0, b > 0 and p, q ∈ [1, +∞], we determine the measurable functions f on ℝ such that E
1/4a
−1
f ∈ L
α,β
p
(ℝ) and e
bλ
2
ℱf ∈ L
σ
q
(ℝ), where E
t
, t > 0, L
α,β
p
(ℝ), p ∈ [1, +∞], and L
σ
q
(ℝ), q ∈ [1, +∞], are respectively the heat kernel and the Lebesgue spaces associated with the Jacobi-Dunkl operator.
*
E-mail: fredj.chouchane@ipeim.rnu.tn
†
E-mail: maher.mili@fsm.rnu.tn
‡
E-mail: mohamed.sifi@fst.rnu.tn |
|---|---|
| AbstractList | In this paper, we give a generalization of Hardy's theorem for the Jacobi-Dunkl transform ℱ on ℝ. More precisely for all a > 0, b > 0 and p, q ∈ [1, +∞], we determine the measurable functions f on ℝ such that E
1/4a
−1
f ∈ L
α,β
p
(ℝ) and e
bλ
2
ℱf ∈ L
σ
q
(ℝ), where E
t
, t > 0, L
α,β
p
(ℝ), p ∈ [1, +∞], and L
σ
q
(ℝ), q ∈ [1, +∞], are respectively the heat kernel and the Lebesgue spaces associated with the Jacobi-Dunkl operator.
*
E-mail: fredj.chouchane@ipeim.rnu.tn
†
E-mail: maher.mili@fsm.rnu.tn
‡
E-mail: mohamed.sifi@fst.rnu.tn |
| Author | Chouchane, F. Trimèche‡, K. Mili†, M. |
| Author_xml | – sequence: 1 givenname: F. surname: Chouchane fullname: Chouchane, F. organization: Preparatory Institute for Engineer Studies of Monastir – sequence: 2 givenname: M. surname: Mili† fullname: Mili†, M. organization: Faculty of Sciences of Monastir , Department of Mathematics – sequence: 3 givenname: K. surname: Trimèche‡ fullname: Trimèche‡, K. organization: Faculty of Sciences of Tunis , Department of Mathematics |
| BookMark | eNqFkEtPwzAQhC1UJNrCP-DgG6fAOo4dhwtU5VFQJS5wtuzYFoHUruzw6L_HVTlW6mlH2m9GuzNBIx-8ReicwCUBAVcEOCsrDpQAAOEAvIEjNCZVzQtRNmSUdUaKzDQnaJLSR8Yoq9kY3c48XuI1_rYxdcHj4PBCRbO5SHh4tyHaFXYhbjV-Vm3QXXH35T97PETlU96sTtGxU32yZ_9zit4e7l_ni2L58vg0ny2LthRiKEqnDRFEA2tqzlyrqQPNDDEcrAAD1moODYBx2tWt0JUlVKuqssxxThWjU1TtctsYUorWyXXsVipuJAG5bUHuayHbbna2zm-vVT8h9kYOatOH6PIPbZckPZBwfTBhn1EOvwP9A83kdvc |
| CitedBy_id | crossref_primary_10_1016_j_crma_2005_06_016 crossref_primary_10_1515_apam_2010_035 crossref_primary_10_1080_10652460701318244 crossref_primary_10_1007_s11118_006_9012_6 crossref_primary_10_1007_s11139_009_9171_3 crossref_primary_10_1186_s13662_021_03512_8 crossref_primary_10_1016_j_amc_2007_08_040 crossref_primary_10_1007_s11868_023_00515_9 crossref_primary_10_1080_10652460701699643 crossref_primary_10_1007_s13540_022_00102_7 crossref_primary_10_1155_2022_2835927 |
| Cites_doi | 10.1017/S1446788700001579 10.1112/jlms/s1-8.3.227 10.1007/BF02880360 10.1007/BF02386203 10.1142/S0219530503000247 10.1016/S1631-073X(02)02361-0 10.1007/BF01889609 |
| ContentType | Journal Article |
| Copyright | Copyright Taylor & Francis Group, LLC 2004 |
| Copyright_xml | – notice: Copyright Taylor & Francis Group, LLC 2004 |
| DBID | AAYXX CITATION |
| DOI | 10.1080/10652460310001600690 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1476-8291 |
| EndPage | 237 |
| ExternalDocumentID | 10_1080_10652460310001600690 9612605 |
| Genre | Original Articles |
| GroupedDBID | .7F .QJ 0BK 0R~ 29J 30N 4.4 5GY 5VS AAAVI AAENE AAJMT AALDU AAMIU AAPUL AAQRR ABBKH ABCCY ABFIM ABHAV ABJVF ABLIJ ABPEM ABPTK ABQHQ ABTAI ABXUL ACAGQ ACGEJ ACGFS ACIWK ACTIO ADCVX ADGTB ADXPE AEGYZ AEISY AENEX AEOZL AEPSL AEYOC AFKVX AFOLD AFWLO AGDLA AGMYJ AGROQ AHDLD AHMOU AIJEM AIRXU AJWEG AKBVH AKOOK ALCKM ALMA_UNASSIGNED_HOLDINGS ALQZU AQRUH AVBZW AWYRJ BLEHA CAG CCCUG CE4 COF CRFIH CS3 DGEBU DKSSO DMQIW DU5 EBS EJD E~A E~B FUNRP FVPDL GTTXZ H13 HZ~ H~P IPNFZ J.P KYCEM M4Z NA5 NY~ O9- P2P QCRFL RIG RNANH ROSJB RTWRZ S-T SNACF TEJ TFL TFT TFW TOXWX TTHFI TWF UT5 UU3 V1K ZGOLN ~S~ 07G 1TA AAIKQ AAKBW AAYXX ABJNI ABPAQ ABXYU ACGEE AEUMN AGCQS AGLEN AHDZW AMXXU BCCOT BPLKW C06 CITATION DWIFK HF~ IVXBP LJTGL NUSFT TAQ TBQAZ TDBHL TFMCV TUROJ UB9 UU8 V3K V4Q |
| ID | FETCH-LOGICAL-c288t-2fbd181b059765fcb3f0b5d1d60e80d0eeb60900dfbf7c8b4e13ba44e5f663a53 |
| ISSN | 1065-2469 |
| IngestDate | Thu Sep 12 16:40:25 EDT 2024 Tue Jun 13 19:48:58 EDT 2023 Mon May 13 12:09:03 EDT 2019 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c288t-2fbd181b059765fcb3f0b5d1d60e80d0eeb60900dfbf7c8b4e13ba44e5f663a53 |
| PageCount | 13 |
| ParticipantIDs | crossref_primary_10_1080_10652460310001600690 informaworld_taylorfrancis_310_1080_10652460310001600690 |
| PublicationCentury | 2000 |
| PublicationDate | 6/1/2004 2004-06-00 |
| PublicationDateYYYYMMDD | 2004-06-01 |
| PublicationDate_xml | – month: 06 year: 2004 text: 6/1/2004 day: 01 |
| PublicationDecade | 2000 |
| PublicationTitle | Integral transforms and special functions |
| PublicationYear | 2004 |
| Publisher | Taylor & Francis Group |
| Publisher_xml | – name: Taylor & Francis Group |
| References | b3 b4 b6 b7 b8 Cowling M. G. (b2) 1983 b1 Gallardo L. (b5) 2002; 334 Trimèche K. (b9) 1997 |
| References_xml | – ident: b3 doi: 10.1017/S1446788700001579 – ident: b6 doi: 10.1112/jlms/s1-8.3.227 – ident: b8 doi: 10.1007/BF02880360 – ident: b7 doi: 10.1007/BF02386203 – volume-title: Generalized Wavelets and Hypergroups year: 1997 ident: b9 contributor: fullname: Trimèche K. – ident: b1 doi: 10.1142/S0219530503000247 – volume: 334 start-page: 849 year: 2002 ident: b5 publication-title: C.R. Acad. Sci. Paris doi: 10.1016/S1631-073X(02)02361-0 contributor: fullname: Gallardo L. – ident: b4 doi: 10.1007/BF01889609 – start-page: pp. 443–449 volume-title: Lecture Notes in Math. 992 year: 1983 ident: b2 contributor: fullname: Cowling M. G. |
| SSID | ssj0013575 |
| Score | 1.7034444 |
| Snippet | In this paper, we give a generalization of Hardy's theorem for the Jacobi-Dunkl transform ℱ on ℝ. More precisely for all a > 0, b > 0 and p, q ∈ [1, +∞], we... |
| SourceID | crossref informaworld |
| SourceType | Aggregation Database Enrichment Source Publisher |
| StartPage | 225 |
| SubjectTerms | Hardy's theorem Jacobi-Dunkl transform |
| Title | An L p version of Hardy's theorem for the Jacobi-Dunkl transform |
| URI | https://www.tandfonline.com/doi/abs/10.1080/10652460310001600690 |
| Volume | 15 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3Na9swFBehvWyH0X2xrOvQYbBDcCZZku3cavZBVtqdUlZ2CZYtQdjqhMZtx_76PX1EVmgoWy_CyJZl9H5--unpvSeE3qVapizXPKkVIbBAaaqkooDlmqZNRZu0kja26uxbNj3nJxfiYjC4jaNLOjmu_-yMK3mIVKEO5GqiZP9DsuGlUAHXIF8oQcJQ_pOMy3Z0OlqNbpzNy9rk3UZ8vvYRipfBjfAEVJ9cJEBYfxr3ck9XY2761WWOiO66_M1rd0T9yEyBvXnPugQsr03gsPMQHgfZLX4tvA9FSazBNdyaXS0u7dZ8AVjZPEOtshlv2R947ydlETO7cxRIZDVzOpUYRzruTmQZK1fH8ywpUndQV1DEIgIci7Wqi432E3TqssTc0f3OWdL0Bp0Ru3FBM5uJuZ_rggfiBJhdZnLf7qf5RMCqfb-cfvrxvd-AEjZHc_j2TdRlQT7s6mGL1WzlvI3YyuwAPfHLDFw6zDxFA9U-Q4_PQo7e9XN0XLb4FK-wRw9eamzR836NPXYwvN9c4xg7OKDjBTr_8nn2cZr48zSSOi2KLoH_sgFCJ4FR55nQtWSaSNHQJiOqIA1RSmZkQkijpc7rQnJFmaw4V0IDL60Ee4n22mWrXiFMKauYygUwLCCwGRQpaYw61xLWB4oPUbIZj_nKpU2ZU5-Ndtf4DRGLB23eWVRpB6idLebd726Iintasfs6fP3wpofoUf8fvEF73dW1OgJm2sm3HkV_AcIPgX8 |
| link.rule.ids | 315,786,790,27957,27958,60241,61030 |
| linkProvider | Library Specific Holdings |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwED5BGYCBN6I8PSAxpXLiJE03KkRVStupldiiOLYlBKQVTRHi13O2E2hR6QBLkuWS2L7zfT7ffQa49BT3WF35TiopxQWKSJzERV1OXU8krvASbmqrev2wPfQ7D0GZTTgp0ir1GlpZoggzV2vj1sHoMiUO72Hg-fp8ZANZDNvuKqyF6G-0bTLa_95ICAzXrpZwUKRRVs_98pY57zTHXTrjdVrbwMv_tckmT7Vpzmvpxw8qx381aAe2CkxKmlaJdmFFZnuw2fsidJ3sw3UzI10yJm82vEZGipg9_6sJsaWQLwQboZ9JB-dY_uggMn56JnmJiw9g2Lod3LSd4vAFJ_WiKHdwEAV6f47wqx4GKuVMUR4IV4RURlRQKXlIG5QKxVU9jbgvXcYT35eBQhCTBOwQKtkok0dAXJclTNYDdMeIdkK8eFRo21ccwaT0q-CUnR6PLcdG7BbUpYt6pgpsdmTi3MQ2lD2IZKFEnL_nVYiWSLFlHzz-u-gFrLcHvW7cvevfn8CGzfvRMZxTqOSvU3mGkCbn50ZpPwENI-X8 |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwED5BkRAMvBHl6QGJKZXzcJpuVEAFpa0YqNQtimNbQoW0oi5C_HrOTgMtKh1gSbJcEttn3-fz3XcA557inl9VgZNKSnGDIhIncVGXU9cTiSu8hNvcqnYnvO0GzR7rTWXxm7BKs4dWOVGEXavN5B4KVUTE4T1kXmDKI1vEYsl2l2ElNBWzTBIH7XyfIzBLtWskHBSpFclzv7xlxjjNUJdOGZ3GJiTF7-axJv3KWPNK-vGDyfE_7dmCjQkiJfVchbZhSWY7sN7-onMd7cJlPSMtMiRvuXONDBSxJ_4XI5InQr4QbIN5Jk1cYfmTg7i4_0x0gYr3oNu4eby6dSalF5zUiyLt4BAKtP0cwVc1ZCrlvqKcCVeEVEZUUCl5SGuUCsVVNY14IF2fJ0EgmUIIkzB_H0rZIJMHQFzXT3xZZWiMEeuEePGoMDNfcYSSMiiDU_R5PMwZNmJ3Qlw6r2fK4E8PTKytZ0PlZUjmSsT6XZchWiDlL_rg4d9Fz2D14boRt-4690ewlgf9GAfOMZT061ieIJ7R_NSq7CdVY-Sp |
| 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=An+L+p+version+of+Hardy%27s+theorem+for+the+Jacobi-Dunkl+transform&rft.jtitle=Integral+transforms+and+special+functions&rft.au=Chouchane%2C+F.&rft.au=Mili%E2%80%A0%2C+M.&rft.au=Trim%C3%A8che%E2%80%A1%2C+K.&rft.date=2004-06-01&rft.pub=Taylor+%26+Francis+Group&rft.issn=1065-2469&rft.eissn=1476-8291&rft.volume=15&rft.issue=3&rft.spage=225&rft.epage=237&rft_id=info:doi/10.1080%2F10652460310001600690&rft.externalDocID=9612605 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1065-2469&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1065-2469&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1065-2469&client=summon |