SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN OVER NONDOUBLING MEASURE SPACES

DOI10.1017/S0004972715001331zbMath1354.46036OpenAlexW2279218675MaRDI QIDQ2786585

Tetsu Shimomura, Takao Ohno

Publication date: 15 February 2016

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972715001331

zbMATH Keywords

Sobolev inequalityRiesz potentialmetric measure spacevariable exponentnondoubling measure

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (14)

Sobolev's inequality in central Herz-Morrey-Musielak-Orlicz spaces over metric measure spaces ⋮ On Sobolev-type inequalities on Morrey spaces of an integral form ⋮ Trudinger's inequality on Musielak-Orlicz-Morrey spaces over non-doubling metric measure spaces ⋮ Trudinger's inequality for Riesz potentials on Musielak-Orlicz spaces over metric measure spaces ⋮ Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces ⋮ Continuity of generalized Riesz potentials for double phase functionals with variable exponents over metric measure spaces ⋮ Unnamed Item ⋮ Maximal operator on Orlicz spaces of two variable exponents over unbounded quasi-metric measure spaces ⋮ Fractional maximal operator on Musielak-Orlicz spaces over unbounded quasi-metric measure spaces ⋮ Continuity of generalized Riesz potentials for double phase functionals ⋮ Maximal and Riesz potential operators on Musielak-Orlicz spaces over metric measure spaces ⋮ Trudinger-type inequalities for variable Riesz potentials of functions in Musielak-Orlicz-Morrey spaces over metric measure spaces ⋮ Generalized Riesz potentials of functions in Morrey spaces \(L^{(1, \varphi;\kappa)}(G)\) over non-doubling measure spaces ⋮ On Trudinger-type Inequalities in Orlicz-Morrey Spaces of an Integral Form

Cites Work

• Unnamed Item
• Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents
• Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces
• Variable Lebesgue spaces. Foundations and harmonic analysis
• Lebesgue and Sobolev spaces with variable exponents
• Nonlinear potential theory on metric spaces
• Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent
• Weak type \(L^ 1\) estimates for maximal functions on non-compact symmetric spaces
• Sharp estimates of the modified Hardy-Littlewood maximal operator on the nonhomogeneous space via covering lemmas
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)

This page was built for publication: SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN OVER NONDOUBLING MEASURE SPACES