Characterization of Besov spaces associated with parabolic sections
type: Item
instance of: scholarly article
title: Characterization of Besov spaces associated with parabolic sections
zbMATH Open document ID: 1469.46029
author: Chin-Cheng Lin
author: Meng Qu
author: Meifang Cheng
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-03-03T00:00:00Z
review text: The authors prove some topological properties of Besov spaces associated with a family of parabolic sections described by monotonic increasing functions. Such functional structure is known to be closely related to the study of the parabolic Monge-Ampère equation. The main results are contained in Theorems~1.5, 1.8 and~1.11. At first the authors prove a duality pairing between Besov spaces by using an approximation of the identity. Then, some duality results for Besov spaces are proved using only the doubling property. The third main result of this paper concerns a continuous embedding between Besov spaces which they prove coupling the doubling property with a lower bound condition. Given these Besov spaces associated with the introduced family of parabolic sections, many problems and challenges can be raised such as the regularity of solutions to the parabolic Monge-Ampère equation with initial data in Besov spaces. I think that this paper will be of great interest.
reviewed by: Ahmed Youssfi
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35K96
zbMATH DE Number: 7317193
zbMATH Keywords: Besov spaces
zbMATH Keywords: Calderón reproducing formula
zbMATH Keywords: embedding theorem
zbMATH Keywords: Monge-Ampère equation
zbMATH Keywords: parabolic sections
MaRDI profile type: Publication
full work available at URL: j.jmaa.2020.124871
OpenAlex ID: W3112623261
cites work: Balls and quasi-metrics: A space of homogeneous type modeling the real analysis related to the Monge-Ampère equation
cites work: Real analysis related to the Monge-Ampère equation
cites work: Properties of the solutions of the linearized Monge-Ampere equation
cites work: Q4287762
cites work: Extensions of Hardy spaces and their use in analysis
cites work: Heat kernel generated frames in the setting of Dirichlet spaces
cites work: Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation. (Calderón-Zygmund operators, para-accretive functions and interpolation)
cites work: \(C^{1,\alpha }\) regularity of solutions to parabolic Monge-Ampère equations
cites work: \(W^{2,p}\) estimates for the parabolic Monge-Ampère equation
cites work: Sobolev embeddings, extensions and measure density condition
cites work: The Embedding Theorem for the Besov and Triebel-Lizorkin Spaces on Spaces of Homogeneous Type
cites work: Inhomogeneous Calderón reproducing formula on spaces of homogeneous type
cites work: Q4719275
cites work: A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot-Carathéodory spaces
cites work: Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces
cites work: Harnack inequality for the linearized parabolic Monge-Ampère equation
cites work: Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation
cites work: Characterization of Campanato spaces associated with parabolic sections
cites work: Lipschitz functions on spaces of homogeneous type
cites work: Q3728446
cites work: Aspects of Sobolev-type inequalities
cites work: Regularity results on the parabolic Monge-Ampère equation with \(VMO\) type data
cites work: Q3336200
cites work: Deforming a hypersurface by its Gauss-Kronecker curvature
cites work: On an Aleksandrov-Bakel'Man Type Maximum Principle for Second-Order Parabolic Equations
cites work: Q4696906
cites work: Q3141797
cites work: Q5620934
DOI: 10.1016/J.JMAA.2020.124871
description: scientific article; zbMATH DE number 7317193