Regularity of maximal functions on Hardy-Sobolev spaces
| Autor: | Carlos Pérez, Mateus Sousa, Olli Saari, Tiago Picon |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics::Functional Analysis
General Mathematics 010102 general mathematics Type (model theory) 01 natural sciences OPERADORES Convolution Combinatorics Sobolev space Homogeneous Mathematics - Classical Analysis and ODEs Bounded function 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics 46E35 (primary) Maximal function 010307 mathematical physics 42B30 0101 mathematics 42B25 42B25 42B30 46E35 Mathematics 42B35 |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy-Sobolev spaces $\dot{H}^{1,p}(\mathbb{R}^d)$ when $1/p < 1+1/d$. This range of exponents is sharp. As a by-product of the proof, we obtain similar results for the local Hardy-Sobolev spaces $\dot{h}^{1,p}(\mathbb{R}^d)$ in the same range of exponents. 10 pages. Corrected the choice of a constant in the proof of Theorem 1 and a few typos |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|