Fractional and hypersingular operators in variable exponent spaces on metric measure spaces

DOI10.1007/s00009-009-0006-7zbMath1182.43011OpenAlexW2123921154MaRDI QIDQ2390701

Alexandre Almeida, Stefan G. Samko

Publication date: 3 August 2009

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-009-0006-7

zbMATH Keywords

hypersingular integralmaximal functionsfractional integralsvariable exponentsmetric measure spaceAhlfors regularity

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractional derivatives and integrals (26A33) Harmonic analysis on homogeneous spaces (43A85) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (12)

Two-weight norm inequalities for potential type and maximal operators in a metric space ⋮ Maximal operator in variable exponent generalized Morrey spaces on quasi-metric measure space ⋮ Unnamed Item ⋮ Potential operators in variable exponent Lebesgue spaces: two-weight estimates ⋮ Fractional action cosmology with variable order parameter ⋮ Unnamed Item ⋮ The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type ⋮ Fractional-in-time and multifractional-in-space stochastic partial differential equations ⋮ Fractional Variational Calculus of Variable Order ⋮ Extended algorithms for approximating variable order fractional derivatives with applications ⋮ Unnamed Item ⋮ Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Traces of Sobolev functions on fractal type sets and characterization of extension domains
• Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent
• Characterization of Riesz and Bessel potentials on variable Lebesgue spaces
• Operators of harmonic analysis in weighted spaces with non-standard growth
• Embeddings of variable Hajłasz-Sobolev spaces into Hölder spaces of variable order
• Hölder quasicontinuity of Sobolev functions on metric spaces
• Hardy's inequalities for Sobolev functions
• On Sobolev theorem for Riesz-type potentials in Lebesgue spaces with variable exponent
• Lectures on analysis on metric spaces
• Continuity of Sobolev functions of variable exponent on metric spaces
• Potential-type operators in \(L^{p(x)}\) spaces
• Maximal and fractional operators in weighted \(L^{p(x)}\) spaces
• Fractional integration and differentiation of variable order
• Fractional integration operator of variable order in the Hölder spaces \(H^{\lambda (x)}\)
• Sobolev spaces on an arbitrary metric space
• Pointwise inequalities in variable Sobolev spaces and applications
• Variable exponent Sobolev spaces on metric measure spaces
• On some weighted inequalities for fractional integrals on nonhomogeneous spaces
• Sobolev embeddings in metric measure spaces with variable dimension
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Sobolev's inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
• Extensions of Hardy spaces and their use in analysis
• Convolution and potential type operators inL^p(x)(Rⁿ)
• Sobolev met Poincaré
• On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators
• Boundedness properties of fractional integral operators associated to non-doubling measures
• Weighted criteria for generalized fractional maximal functions and potentials in Lebesgue spaces with variable exponent

This page was built for publication: Fractional and hypersingular operators in variable exponent spaces on metric measure spaces