Fractional Orlicz-Sobolev embeddings into Campanato type spaces

2025/06/16 by Angela Alberico, Andrea Cianchi, Alberico, Angela +5
Engineering · Mathematics · #46E30 #46E35 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2506.13669

openalex publication_date 2025/06/16 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

Optimal embeddings for fractional Orlicz-Sobolev spaces into (generalized) Campanato spaces on the Euclidean space are exhibited. Embeddings into vanishing Campanato spaces are also characterized. Sharp embeddings into BMO(\mathbb Rⁿ) and VMO(\mathbb Rⁿ) are derived as special instances. Dissimilarities to corresponding embeddings for classical fractional Sobolev spaces are pointed out.

Citations

• On the modulus of continuity of fractional Orlicz-Sobolev functions
• Boundedness of functions in fractional Orlicz-Sobolev spaces
• Homogeneous eigenvalue problems in Orlicz-Sobolev spaces
• Harnack inequality for nonlocal problems with non-standard growth
• Harnack inequality for the nonlocal equations with general growth
• Existence and multiplicity of solutions for a Dirichlet problem in Fractional Orlicz- Sobolev spaces
• Local Hölder continuity for fractional nonlocal equations with general growth
• Compact embedding theorems and a Lions' type Lemma for fractional\n Orlicz-Sobolev spaces
• Interior and up to the boundary regularity for the fractional g-Laplacian: the convex case
• Fractional eigenvalues in Orlicz spaces with no Δ₂ condition
• On the limit as s→ 0⁺ of fractional Orlicz-Sobolev spaces
• Fractional Orlicz-Sobolev embeddings
• Embedding theorems in the fractional Orlicz-Sobolev space and\n applications to non-local problems
• A Pólya-Szegö principle for general fractional Orlicz-Sobolev spaces
• Fractional order Orlicz-Sobolev spaces
• Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant

Related

• Fractional Orlicz-Sobolev embeddings
• Boundedness of functions in fractional Orlicz-Sobolev spaces
• Higher-order Sobolev embeddings into spaces of Campanato and Morrey type
• Inclusion relations among fractional Orlicz-Sobolev spaces and a Littlewood-Paley characterization
• Introduction to fractional Orlicz-Sobolev spaces