, Volume 82, Issue 1, pp 40-50

A class of bounded operators on Sobolev spaces

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract.

We describe a class of nonlinear operators which are bounded on the Sobolev spaces \( H^{s}_{p}(\mathbb{R}^n) \) , for \( 0 \leq s \leq 1 \) and 1 < p < \( \infty \) . As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on \( H^{s}_{p}(\mathbb{R}^n) \) , for \( 0 \leq s \leq 1 \) and 1 < p < \( \infty \) ; this extends the result of J. Kinnunen [7], valid for s = 1.

Received: 5 December 2000