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Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces [PDF]
Analysis and Geometry in Metric Spaces, 2016 This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the space.
Hakkarainen Heikki +3 more
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Asymptotic Normality and Convergence Rates for Tsallis Entropy Estimators via Stabilization Techniques [PDF]
EntropyWe study nearest-neighbor-based estimators of Tsallis entropy associated with Poisson and binomial point processes on general metric measure spaces. In this study, by combining existing stabilization methods with the validation of the estimator’s local k-
Mehmet Sıddık Çadırcı +1 more
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Density and extension of differentiable functions on metric measure spaces [PDF]
, 2021 We consider vector valued mappings de ned on metric measure spaces with a measurable differ-entiable structure and study both approximations by nicer mappings and regular extensions of the givenmappings when de ned on closed subsets.
Espínola García, Rafael +1 more
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Nonlinear variational problems on metric measure spaces [PDF]
, 2022 This dissertation studies existence and regularity properties of functions related to the calculus of variations on metric measure spaces that support a weak Poincaré inequality and doubling measure.
Pacchiano Camacho, Cintia
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Sobolev Spaces in Extended Metric-Measure Spaces [PDF]
, 2021 These lecture notes contain an extended version of the material presented in the C.I.M.E. summer course in 2017. The aim is to give a detailed introduction to the metric Sobolev theory. The notes are divided in four main parts.
Savaré, Giuseppe, Giuseppe Savaré
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Lp Smoothness on Weighted Besov–Triebel–Lizorkin Spaces in terms of Sharp Maximal Functions
Journal of Mathematics, 2021 It is known, in harmonic analysis theory, that maximal operators measure local smoothness of Lp functions. These operators are used to study many important problems of function theory such as the embedding theorems of Sobolev type and description of ...
Ferit Gürbüz, Ahmed Loulit
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Журнал Белорусского государственного университета: Математика, информатика, 2020 Let (X, d, µ) be a doubling metric measure space with doubling dimension γ, i. e. for any balls B(x, R) and B(x, r), r < R, following inequality holds µ(B(x, R)) ≤ aµ (R/r)γµ(B(x, r)) for some positive constants γ and aµ.
Sergey A. Bondarev
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Variational solutions to the total variation flow on metric measure spaces [PDF]
, 2022 We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincar\'e inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian spaces and ...
Buffa, Vito +3 more
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Land, 2023 The degree of coordination between the supply and demand for urban green spaces serves as a vital metric for evaluating urban ecological development and the well-being of residents.
Yukuan Dong +3 more
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Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces [PDF]
, 2021 We study commutators of weighted fractional Hardy-type operators within the frameworks of local generalized Morrey spaces over quasi-metric measure spaces for a certain class of “radial” weights.
Samko, Natasha Gabatsuyevna
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