Results 11 to 20 of about 97 (96)

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

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

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

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

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
doaj   +1 more source

On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators

Journal of Function Spaces and Applications, 2008
A construction of Triebel-Lizorkin type spaces associated with flexible decompositions of the frequency space ℝd is considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations on ℝd and a ...
Lasse Borup, Morten Nielsen
doaj   +1 more source

Elliptic problems in Besov and Sobolev—Triebel—Lizorkin spaces of low regularity

Доповiдi Нацiональної академiї наук України, 2021
Elliptic problems with additional unknown distributions in boundary conditions are investigated in Besov and Sobolev–Triebel–Lizorkin spaces of low regularity, specifically of an arbitrary negative order.
I.S. Chepurukhina, A.A. Murach
doaj   +1 more source