Complex interpolation of Besov spaces and Triebel-Lizorkin spaces with variable exponents

DOI10.1016/j.jmaa.2011.09.023zbMath1242.46044OpenAlexW2007822226MaRDI QIDQ655471

Yoshihiro Sawano, Takahiro Noi

Publication date: 4 January 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.09.023

zbMATH Keywords

Triebel-Lizorkin spacesBesov spacesatomscomplex interpolationvariable exponent function spaces

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Interpolation between normed linear spaces (46B70)

Related Items (18)

Trace and extension operators for Besov spaces and Triebel-Lizorkin spaces with variable exponents ⋮ Complex interpolation of variable Triebel-Lizorkin spaces ⋮ Anisotropic variable Hardy-Lorentz spaces and their real interpolation ⋮ Precompact sets, boundedness, and compactness of commutators for singular integrals in variable Morrey spaces ⋮ Musielak-Orlicz Besov-type and Triebel-Lizorkin-type spaces ⋮ Littlewood-Paley and finite atomic characterizations of anisotropic variable Hardy-Lorentz spaces and their applications ⋮ Complex interpolation of smoothness Morrey subspaces ⋮ Weighted local Hardy spaces with variable exponents ⋮ Complex interpolation of various subspaces of Morrey spaces ⋮ Weighted Besov spaces with variable exponents ⋮ Variable anisotropic Hardy spaces and their applications ⋮ Density, duality and preduality in grand variable exponent Lebesgue and Morrey spaces ⋮ Besov-type spaces with variable smoothness and integrability ⋮ Duality of Besov, Triebel-Lizorkin and Herz spaces with variable exponents ⋮ Extension of variable Triebel-Lizorkin-type space on domains ⋮ Hardy spaces with variable exponents on RD-spaces and applications ⋮ Local Muckenhoupt class for variable exponents ⋮ Triebel-Lizorkin type spaces with variable exponents

Cites Work

• Continuous characterizations of Besov-Lizorkin-Triebel spaces and new interpretations as coorbits
• Hardy spaces with variable exponents and generalized Campanato spaces
• Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type
• Atomic, molecular and wavelet decomposition of 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability
• A discrete transform and decompositions of distribution spaces
• Besov spaces with variable smoothness and integrability
• Function spaces of variable smoothness and integrability
• An example of a space of \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded
• On the modeling of electrorheological materials
• Maximal functions on Musielak--Orlicz spaces and generalized Lebesgue spaces
• Fourier multiplier theorems for Besov and Triebel-Lizorkin spaces with variable exponents
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