Recent Developments of Function Spaces and Their Applications I

• Format: eBook
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: (localized) John–Nirenberg–Campanato space; (mixed-norm) Hardy space; anisotropic log-potential; anisotropy; annulus body; besov space; bilinear estimate; block spaces; BMO; Calderón operator; Calderón–Zygmund operator; capacity; commutator; commutators; compact manifolds; congruent cube; continuous ellipsoid cover; convexification; cube; differential operators; Dirichlet problem; dual log-mixed volume; duality; Euclidean space; expansive matrix; extrapolation; fractional Laplacian; generalized smoothness; Hajłasz–Besov space; Hajłasz–Sobolev space; Hajłasz–Triebel–Lizorkin space; Hardy inequality; hardy space; Hardy’s inequality; homogeneous group; JNp; Lebesgue point; local block space; local Morrey space; Mathematics and Science; maximal function; metric measure space; meyer wavelet; molecule; Morrey space; Morrey spaces; optimal polynomial inequality; paraproduct; pointwise multipliers; real interpolation; Reference, Information and Interdisciplinary subjects; Research and information: general; Riesz potential; Riesz–Morrey space; Schrödinger equation; Sobolev spaces; space of homogeneous type; T theorem; tensor bundles; Triebel–Lizorkin space; uniform domain; vanishing John–Nirenberg space; variable Lebesgue space
• ISBN: 9783036540184; 3036540172; 3036540180; 9783036540177
• DOI: 10.3390/books978-3-0365-4018-4

This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John–Nirenberg spaces, Sobolev spaces, and Besov and Triebel–Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calderón operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schrödinger equation.