Some characterizations of upper doubling conditions on metric measure spaces
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201400347
Abstract: We provide several equivalent characterizations for the upper doubling condition introduced in the framework of T. Hytonen for non-homogeneous metric measure spaces. We also introduce the “smooth strong upper doubling” condition and provide equivalent characterizations,… read more here.
Keywords: upper doubling; characterizations upper; metric measure; doubling conditions ... See more keywords
Universal inequalities on complete noncompact smooth metric measure spaces
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DOI: 10.1007/s00013-017-1099-z
Abstract: In this paper, we obtain universal inequalities for the eigenvalues of the Dirichlet problem and clamped plate problem of drifting Laplacian on ($$n+1$$n+1)-dimensional ($$n\ge 4$$n≥4) complete noncompact simply connected smooth metric measure spaces which meet… read more here.
Keywords: complete noncompact; metric measure; smooth metric; universal inequalities ... See more keywords
Characterizations of weak reverse Hölder inequalities on metric measure spaces
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DOI: 10.1007/s00209-022-02976-y
Abstract: We present ten different characterizations of functions satisfying a weak reverse Hölder inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class… read more here.
Keywords: reverse lder; weak reverse; measure; infty weights ... See more keywords
On the domains of Dirichlet forms on metric measure spaces
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DOI: 10.1007/s00209-022-02987-9
Abstract: We prove that the domain of the local Dirichlet form is strictly contained in the domain of any stable-like non-local Dirichlet form on general metric measure spaces. read more here.
Keywords: measure spaces; domains dirichlet; dirichlet forms; metric measure ... See more keywords
Existence of parabolic minimizers to the total variation flow on metric measure spaces
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DOI: 10.1007/s00229-021-01350-2
Abstract: We give an existence proof for variational solutions u associated to the total variation flow. Here, the functions being considered are defined on a metric measure space $$({\mathcal {X}}, d, \mu )$$ ( X ,… read more here.
Keywords: variation flow; total variation; parabolic minimizers; metric measure ... See more keywords
Spectral Stability of Metric-Measure Laplacians
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DOI: 10.1007/s11856-019-1865-7
Abstract: We consider a “convolution mm-Laplacian” operator on metric-measure spaces and study its spectral properties. The definition is based on averaging over small metric balls. For reasonably nice metric-measure spaces we prove stability of convolution Laplacian’s… read more here.
Keywords: stability metric; measure laplacians; measure; metric measure ... See more keywords
Weighted Morrey spaces on non-homogeneous metric measure spaces
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.03.023
Abstract: Abstract Let ( X , d , μ ) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. In this setting, the authors introduce the weighted Morrey space… read more here.
Keywords: morrey spaces; weighted morrey; spaces non; non homogeneous ... See more keywords
N-Lusin property in metric measure spaces: A new sufficient condition
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DOI: 10.1515/forum-2018-0016
Abstract: In this work, we are concerned with the study of the N-Lusin property in metric measure spaces. A map satisfies that property if sets of measure zero are mapped to sets of measure zero. We… read more here.
Keywords: measure; lusin property; property; metric measure ... See more keywords