Sobolev spaces on Lipschitz curves

María Cristina Pereyra

Vol. 172 (1996), No. 2, 553–589

DOI: 10.2140/pjm.1996.172.553

Abstract

We study Sobolev spaces on Lipschitz graphs Γ, by means of a square function of a geometric second difference. Given a function in the Sobolev space W^1,p(Γ) we show that the geometric square function is also in L^p(Γ). For p = 2 we prove a dyadic analogue of this result, and a partial converse.

Mathematical Subject Classification 2000

Primary: 42B25

Secondary: 46E35

Milestones

Received: 10 September 1993

Revised: 17 July 1995

Published: 1 February 1996