Results 31 to 40 of about 173 (137)
Generalized quasi‐geostrophic equation in critical Lorentz–Besov spaces, based on maximal regularity
Mathematische Nachrichten, Volume 299, Issue 3, Page 637-660, March 2026.Abstract We consider the quasi‐geostrophic equation with its principal part (−Δ)α${(-\mathrm{\Delta})^{\alpha}}$ for α>1/2$\alpha >1/2$ in Rn$\mathbb {R}^n$ with n≥2$n \ge 2$. We show that for every initial data θ0∈Ḃr,q1−2α+nr$\theta _0 \in \dot{B}^{1-2\alpha + \frac{n}{r}}_{r, q}$ with 1
Hideo Kozono +2 more
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On the Fourier transform of measures in Besov spaces
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract We prove quantitative estimates for the decay of the Fourier transform of the Riesz potential of measures that are in homogeneous Besov spaces of the negative exponent: ∥Iαμ̂∥Lp,∞⩽C∥μ∥Mb12supt>0td−β2∥pt*μ∥∞12,$$\begin{align*} \Vert \widehat{I_{\alpha }\mu }\Vert _{L^{p, \infty }} \leqslant C \Vert \mu \Vert _{M_b}^{\frac{1}{2}}{\left(\sup _{t ...
Riju Basak +2 more
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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.Stochastic processes prevail throughout fields as diverse as finance, physics, and biology, demanding increasingly sophisticated mathematical tools. These are the principal components of modeling systems influenced by random forces. The present work offers a structured examination of the solution landscape, progressing from foundational classical ...
Danamma I. Badigannavar +2 more
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.This paper investigates the regularity criteria for the velocity field of three‐dimensional shear‐thinning fluids in the framework of Besov spaces. We obtain that when the specific negative exponent of the velocity field satisfies certain integrability conditions in Besov space, its regularity can be completely characterized by a set of parameter ...
Tianli Li +3 more
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.We investigate the Cauchy problem for the fourth‐order Schrödinger equation with quadratic nonlinearities involving second‐order derivatives: uxxu, uxxū, (ux)2, uūxx, and |ux|2, where u = u(x, t) is a complex‐valued function defined on R×R. The flow map of this Cauchy problem with the nonlinear terms uxxu or uxxū fails to be C2 differentiable at zero ...
Long Xiao, Ting Chen, Xian-Ming Gu
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Random Gel′fand Approximation Between Anisotropic Spaces and Function Spaces With Mixed Smoothness
Journal of Function Spaces, Volume 2026, Issue 1, 2026.This paper investigates the complexity associated with function approximation between anisotropic spaces and spaces of mixed smoothness within the framework of adaptive Monte Carlo methods. Specifically, we analyze the information complexity for approximating function classes of mixed smoothness Fmix,pr(1 ≤ p < ∞) in anisotropic spaces FqR(1 ≤ q ...
Bo Feng +4 more
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Global Solvability of the Generalized Navier−Stokes System in Critical Besov Spaces
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper is devoted to the global solvability of the Navier−Stokes system with a fractional Laplacian (−Δ)α in Rn for n ≥ 2, where the convective term has the form (|u|m−1u)·∇u for m ≥ 1. By establishing the estimates for the difference u1m−1u1−u2m−1u2 in homogeneous Besov spaces and employing the maximal regularity property of (−Δ)α in Lorentz−Besov
Huiyang Zhang +3 more
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Commutators for Fourier multipliers on Besov Spaces
Journal of Approximation Theory, 2004 If T is any bounded linear operator on Besov spaces Bpσj,qj(Rn)(j=0,1, and ...
Joan Cerdà, Joaquim Martín
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MINIMIZERS FOR THE EMBEDDING OF BESOV SPACES
Journal of Applied Analysis & Computation, 2017 Summary: Using the profile decomposition, we will show the relatively compactness of the minimizing sequence to the critical embeddings between Besov spaces, which implies the existence of minimizer of the critical embeddings of Besov spaces \(\dot{B}^{s_1}_{p_1,q_1}\hookrightarrow \dot{B}^{s_2}_{p_2,q_2}\) in \(d\) dimensions with \(s_1-d/p_1=s_2-d ...
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Two–microlocal Besov spaces and wavelets
Revista Matemática Iberoamericana, 2004 We give a characterization of the two-microlocal Besov spaces in terms of the local Besov type conditions. As an easy consequence, we obtain the inclusions between the two-microlocal Besov spaces and the local Besov spaces. These results are natural extensions of those obtained by Jaffard and Meyer, who treated the pointwise Hölder regularity in terms ...
Moritoh, Shinya, Yamada, Tomomi
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