Regularity of maximal functions on Hardy-Sobolev spaces

Abstract

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

References in corpus (3)

• Derivative bounds for fractional maximal functions
• On the variation of maximal operators of convolution type II
• Poincaré inequalities for the maximal function

Cited by in corpus (3)

• Regularity of fractional maximal functions through Fourier multipliers
• Weak differentiability for fractional maximal functions of general $L^p$ functions on domains
• Regularity of maximal operators: recent progress and some open problems