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22 pages, 341 KB

Open AccessArticle

Variable Besov–Morrey Spaces Associated with Operators

by Khedoudj Saibi

Mathematics 2023, 11(9), 2038; https://doi.org/10.3390/math11092038 - 25 Apr 2023

Cited by 4 | Viewed by 1831

Let

(X, d, μ)

be a space of homogenous type and L be a non-negative self-adjoint operator on

L^{2} (X)

with heat kernels satisfying Gaussian upper bounds. In this paper, we introduce the variable Besov–Morrey space [...] Read more.

Let

(X, d, μ)

be a space of homogenous type and L be a non-negative self-adjoint operator on

L^{2} (X)

with heat kernels satisfying Gaussian upper bounds. In this paper, we introduce the variable Besov–Morrey space associated with the operator L and prove that this space can be characterized via the Peetre maximal functions. Then, we establish its atomic decomposition. Full article

(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)

12 pages, 287 KB

Open AccessArticle

An Improved Regularity Criterion for the 3D Magnetic Bénard System in Besov Spaces

by Muhammad Naqeeb, Amjad Hussain and Ahmad M. Alghamdi

Symmetry 2022, 14(9), 1918; https://doi.org/10.3390/sym14091918 - 13 Sep 2022

Cited by 5 | Viewed by 2032

Abstract

This article notably targets the more general (extended) function spaces by investigating the regularity of the weak solutions or turbulent solutions to the Cauchy problem of the 3D magnetic Bénard system by converting it into mathematical symmetric form, in the absence of thermal diffusion, in terms of pressure. In that regard, we successfully improved the results by obtaining sufficient integrable regularity conditions for the pressure and gradient pressure in the homogeneous Besov spaces. Full article

(This article belongs to the Special Issue Symmetries in Evolution Equations and Applications)

14 pages, 324 KB

Open AccessArticle

The Well Posedness for Nonhomogeneous Boussinesq Equations

by Yan Liu and Baiping Ouyang

Symmetry 2021, 13(11), 2110; https://doi.org/10.3390/sym13112110 - 6 Nov 2021

Cited by 1 | Viewed by 1832

Abstract

This paper is devoted to studying the Cauchy problem for non-homogeneous Boussinesq equations. We built the results on the critical Besov spaces [...] Read more.

This paper is devoted to studying the Cauchy problem for non-homogeneous Boussinesq equations. We built the results on the critical Besov spaces

(θ, u) \in L_{T}^{\infty} ({\dot{B}}_{p, 1}^{N / p}) \times L_{T}^{\infty} ({\dot{B}}_{p, 1}^{N / p - 1}) ⋂ L_{T}^{1} ({\dot{B}}_{p, 1}^{N / p + 1})

with

1 < p < 2 N

. We proved the global existence of the solution when the initial velocity is small with respect to the viscosity, as well as the initial temperature approaches a positive constant. Furthermore, we proved the uniqueness for

1 < p \leq N

. Our results can been seen as a version of symmetry in Besov space for the Boussinesq equations. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis)

11 pages, 274 KB

Open AccessArticle

Wavelets and Real Interpolation of Besov Spaces

by Zhenzhen Lou, Qixiang Yang, Jianxun He and Kaili He

Mathematics 2021, 9(18), 2235; https://doi.org/10.3390/math9182235 - 12 Sep 2021

Cited by 2 | Viewed by 2788

Abstract

In view of the importance of Besov space in harmonic analysis, differential equations, and other fields, Jaak Peetre proposed to find a precise description of [...] Read more.

In view of the importance of Besov space in harmonic analysis, differential equations, and other fields, Jaak Peetre proposed to find a precise description of

{(B_{p_{0}}^{s_{0}, q_{0}}, B_{p_{1}}^{s_{1}, q_{1}})}_{θ, r}

. In this paper, we come to consider this problem by wavelets. We apply Meyer wavelets to characterize the real interpolation of homogeneous Besov spaces for the crucial index p and obtain a precise description of

{({\dot{B}}_{p_{0}}^{s, q}, {\dot{B}}_{p_{1}}^{s, q})}_{θ, r}

. Full article

(This article belongs to the Special Issue Recent Developments of Function Spaces and Their Applications I)

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