Results 21 to 30 of about 5,281,258 (136)

Notes on pseudodifferential operators commutators and Lipschitz functions

Open Mathematics, 2023
This article focuses on the boundedness of the commutators generated by pseudodifferential operators with Lipschitz functions and obtains a sufficient condition such that these operators are bounded from Lp(Rn){L}^{p}\left({{\bf{R}}}^{n}) into the ...
Deng Yu-long
doaj   +1 more source

Pointwise characterization of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type [PDF]

Studia Mathematica, 2022
In this article, the authors establish the pointwise characterization of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type via clarifying the relationship among Haj\l asz-Sobolev spaces, Haj\l asz-Besov and Haj\l asz-Triebel-Lizorkin spaces,
R. Alvarado, Fan Wang, Dachun Yang, Wen Yuan   +3 more
semanticscholar   +1 more source

Blow‐up regions for a class of fractional evolution equations with smoothed quadratic nonlinearities

Mathematische Nachrichten, Volume 295, Issue 8, Page 1462-1479, August 2022., 2022
Abstract We consider an n‐dimensional parabolic‐type PDE with a diffusion given by a fractional Laplace operator and with a quadratic nonlinearity of the “gradient” of the solution, convoluted with a term b$\mathfrak {b}$ which can be singular. Our first result is the well‐posedness for this problem: We show existence and uniqueness of a (local in time)
Diego Chamorro, Elena Issoglio
wiley   +1 more source

Triebel-lizorkin space estimates for multilinear operators of sublinear operators [PDF]

, 2003
In this paper, we obtain the continuity for some multilinear operators related to certain non-convolution operators on the Triebel-Lizorkin space. The operators include Littlewood-Paley operator and Marcinkiewicz operator.
Lan-Zhe Liu
semanticscholar   +1 more source

A Measure Characterization of Embedding and Extension Domains for Sobolev, Triebel–Lizorkin, and Besov Spaces on Spaces of Homogeneous Type [PDF]

Journal of Functional Analysis, 2022
In this article, for an optimal range of the smoothness parameter s that depends (quantitatively) on the geometric makeup of the underlying space, the authors identify purely measure theoretic conditions that fully characterize embedding and extension ...
R. Alvarado, Dachun Yang, Wen Yuan
semanticscholar   +1 more source

Maximal regularity for the Cauchy problem of the heat equation in BMO

Mathematische Nachrichten, Volume 295, Issue 7, Page 1406-1442, July 2022., 2022
Abstract We consider maximal regularity for the Cauchy problem of the heat equation in a class of bounded mean oscillations (BMO$BMO$). Maximal regularity for non‐reflexive Banach spaces is not obtained by the established abstract theory. Based on the symmetric characterization of BMO$BMO$‐expression, we obtain maximal regularity for the heat equation ...
Takayoshi Ogawa, Senjo Shimizu
wiley   +1 more source

A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution

Mathematics, 2022
In this article, certain sharp Lp estimates for a specific class of generalized Marcinkiewicz operators with mixed homogeneity associated to surfaces of revolution are established.
Mohammed Ali, Hussain Al-Qassem
doaj   +1 more source

Optimal embeddings for Triebel–Lizorkin and Besov spaces on quasi-metric measure spaces [PDF]

Mathematische Zeitschrift, 2022
In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Hajłasz–Triebel–Lizorkin and Hajłasz–Besov spaces in the general context of quasi-metric ...
R. Alvarado, Dachun Yang, Wen Yuan
semanticscholar   +1 more source

Bochner's subordination and fractional caloric smoothing in Besov and Triebel–Lizorkin spaces

Mathematische Nachrichten, Volume 295, Issue 2, Page 363-376, February 2022., 2022
Abstract We use Bochner's subordination technique to obtain caloric smoothing estimates in Besov‐ and Triebel–Lizorkin spaces. Our new estimates extend known smoothing results for the Gauß–Weierstraß, Cauchy–Poisson and higher‐order generalized Gauß–Weierstraß semigroups.
Victoriya Knopova, René L. Schilling
wiley   +1 more source

The Boundedness of Doob’s Maximal and Fractional Integral Operators for Generalized Grand Morrey‐Martingale Spaces

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this paper, we introduce the generalized grand Morrey spaces in the framework of probability space setting in the spirit of the martingale theory and grand Morrey spaces. The Doob maximal inequalities on the generalized grand Morrey spaces are provided.
Libo Li, Zhiwei Hao, Xinru Ding, Tianqing An   +3 more
wiley   +1 more source