Regularity of Weak Solutions on Besov Spaces via the Continuous Shearlet Transform in Higher Dimensions
Abstract
Abstract The aim of this work is to provide a characterization for the Besov spaces $$B^{r,q}_p(\mathbb {R}^n)$$ B p r , q ( R n ) via the continuous shearlet transform in higher dimensions with isotropic dilations to show the regularity of weak solutions $$u \in W^{m,p}(\mathbb {R}^n)$$ u ∈ W m , p ( R n ) under the equation $$Qu =f$$ Q u = f , so that for a given $$f \in B^{r,q}_p(\mathbb {R}^n)$$ f ∈ B p r , q ( R n ) , $$u \in B^{r+m,q}_p(\mathbb {R}^n)$$ u ∈ B p r + m , q ( R n ) . In this case, $$1< p,q < \infty $$ 1 < p , q < ∞ , $$0< r < 1$$ 0 < r < 1 , and where $$Q = \sum _{\beta \le m}c_{\beta } \partial ^{\beta }$$ Q = ∑ β ≤ m c β ∂ β is a partial differential operator of pure order m with positive constant coefficients $$c_{\beta }$$ c
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Navier-Stokes equation solutions
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Bulletin of the Iranian Mathematical Society.
- Publisher
- Springer Science and Business Media LLC
- Volume
- 52
- Issue
- 3
- Publication date
- 21 May 2026
- Language
- EN