Compactness of embeddings of Sobolev type on metric measure spaces

DOI10.1134/S0001434609110200zbMath1192.46029OpenAlexW2091246059MaRDI QIDQ845212

I. A. Ivanishko, V. G. Krotov

Publication date: 5 February 2010

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434609110200

zbMATH Keywords

Sobolev spaceBorel measureLebesgue measuremetric measure spaceHardy-Littlewood maximal functionHölder classembedding of Sobolev type

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 (11)

Weighted endpoint bounds for the Bergman and Cauchy-Szego projections on domains with near minimal smoothness ⋮ Sobolev embedding theorems and generalizations for functions on a metric measure space ⋮ Sobolev spaces on an arbitrary metric measure space: compactness of embeddings ⋮ The Itô SDEs and Fokker–Planck equations with Osgood and Sobolev coefficients ⋮ Sobolev embedding theorems and their generalizations for maps defined on topological spaces with measures ⋮ Embedding theorems and a variational problem for functions on a metric measure space ⋮ Riesz-Kolmogorov type compactness criteria in function spaces with applications ⋮ Some results for the Szegő and Bergman projections on planar domains ⋮ Hausdorff dimension of Lebesgue sets for \(W \alpha p\) classes on metric spaces ⋮ Maximal Functions Measuring Smoothness ⋮ Poincaré inequalities and compact embeddings from Sobolev type spaces into weighted \(L^q\) spaces on metric spaces

Cites Work

• New characterizations of Hajłasz-Sobolev spaces on metric spaces
• Haar wavelets of higher order on fractals and regularity of functions.
• Lectures on analysis on metric spaces
• Sobolev spaces on an arbitrary metric space
• Generalized Sobolev classes on metric measure spaces
• Maximal functions measuring smoothness
• Sobolev type inequalities for p>0
• Estimates for singular integral operators in terms of maximal functions
• Estimates of maximal functions measuring local smoothness
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