Sobolev embeddings in metric measure spaces with variable dimension

DOI10.1007/s00209-006-0960-8zbMath1109.46037OpenAlexW2060713370MaRDI QIDQ2509054

Visa Latvala, Peter A. Hästö, Petteri Harjulehto

Publication date: 16 October 2006

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-006-0960-8

zbMATH Keywords

Lebesgue spaceHausdorff measureRiesz potentialmetric measure spaceHajlasz spacevariable exponent, variable dimension

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) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (35)

Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials ⋮ Maximal operator in variable exponent generalized Morrey spaces on quasi-metric measure space ⋮ Unnamed Item ⋮ Fractional and hypersingular operators in variable exponent spaces on metric measure spaces ⋮ Ergodic theorem in variable {L}ebesgue spaces ⋮ Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in \(\mathbb{R}^n\) ⋮ Musielak-Orlicz-Sobolev spaces on metric measure spaces ⋮ Trudinger's inequality on Musielak-Orlicz-Morrey spaces over non-doubling metric measure spaces ⋮ Sobolev's inequality in Musielak–Orlicz–Morrey spaces of an integral form ⋮ Trudinger's inequality for Riesz potentials on Musielak-Orlicz spaces over metric measure spaces ⋮ Potential operators in variable exponent Lebesgue spaces: two-weight estimates ⋮ Iterated maximal functions in variable exponent Lebesgue spaces ⋮ Sobolev spaces with variable exponents on complete manifolds ⋮ Looking for compactness in Sobolev spaces on noncompact metric spaces ⋮ Unnamed Item ⋮ The fundamental convergence theorem for \(p(\cdot )\)-superharmonic functions ⋮ The modulus of smoothness in metric spaces and related problems ⋮ Variable Hajłasz-Sobolev spaces on compact metric spaces ⋮ Trudinger's inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces ⋮ The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type ⋮ Maximal and Riesz potential operators on Musielak-Orlicz spaces over metric measure spaces ⋮ Relatively compact sets in variable-exponent Lebesgue spaces ⋮ Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent ⋮ Sobolev spaces with variable exponents on Riemannian manifolds ⋮ Variable exponent Campanato spaces ⋮ Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures ⋮ Almost everything you need to know about relatively compact sets in variable Lebesgue spaces ⋮ Generalized potentials in variable exponent Lebesgue spaces on homogeneous spaces ⋮ Operators of harmonic analysis in weighted spaces with non-standard growth ⋮ Variable exponent Sobolev spaces and regularity of domains ⋮ Embeddings of variable Hajłasz-Sobolev spaces into Hölder spaces of variable order ⋮ SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES ⋮ Two-weight weak type inequality for modified fractional maximal function defined with respect to non-doubling measure and some applications in non-standard Lebesgue spaces ⋮ The maximal operator on weighted variable Lebesgue spaces ⋮ Weighted Morrey spaces of variable exponent and Riesz potentials

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