Some remarks on Campanato Theorem and the Anisotropic Bessel Spaces

2025/05/25 by Hajaiej, H., Leitao, R.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.19289

Abstract

In this paper, we establish an anisotropic version of Campanato Theorem and show that the anisotropic Bessel spaces are continuously embedded in the spaces of Holder continuous functions. As an application of this embedding, we build fundamental solutions for a class of anisotropic fractional Laplacian operators.

Citations

• A regularity theory for parabolic equations with anisotropic non-local operators in L_q(L_p) spaces
• Fundamental solutions and critical Lane-Emden exponents for nonlinear integral operators in cones
• Fully nonlinear integro-differential equations with deforming kernels
• Free boundary problems involving singular weights
• Regularity theory for general stable operators
• Regularity for anisotropic fully nonlinear integro-differential equations
• Hitchhiker's guide to the fractional Sobolev spaces
• Hitchhikerʼs guide to the fractional Sobolev spaces
• Fundamental solutions of homogeneous fully nonlinear elliptic equations
• On the existence of certain singular integrals
• Holder estimates for solutions of integro differential equations like the fractional laplace

Related

• Anisotropic Function Spaces and Elliptic Boundary Value Problems
• On the Hölder regularity for solutions of integro-differential equations like the anisotropic fractional Laplacian
• Extension and embedding theorems for Campanato spaces on C^0,γ domains
• Anisotropic fractional Sobolev spaces with variable exponent and application to nonlocal problems
• Embeddings for anisotropic Besov spaces