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
Boundedness of some convolution-type operators on metric measure spaces
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DOI: 10.1007/s10476-024-00030-z
Abstract: We explore boundedness properties of some natural operators of convolution type in the context of metric measure spaces. Their study is suggested by certain transformations used in computer vision. read more here.
Keywords: type operators; convolution type; metric measure; boundedness convolution ... See more keywords
ESTIMATES OF VARIATIONAL EIGENVALUES ON METRIC MEASURE SPACES
Sign Up to like & getrecommendations! Published in 2025 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-025-07910-1
Abstract: In the article, we study variational eigenvalues on doubling metric measure spaces. We prove the existence of minimizers of variational Neumann (p, q)-eigenvalues on metric measure spaces, and on this base, we obtain estimates of Neumann… read more here.
Keywords: variational eigenvalues; metric measure; eigenvalues metric; estimates variational ... 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
Hardy inequalities on metric measure spaces, IV: The case p=1
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DOI: 10.1515/forum-2023-0319
Abstract: Abstract In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case p = 1 {p=1} and 1 ≤ q < ∞ {1\leq q read more here.
Keywords: metric measure; case; inequalities metric; hardy inequalities ... See more keywords