Pointwise multipliers of Lizorkin-Triebel spaces

Preprint series: 99-16, Analysis

The paper is published: Oper. Theory Adv. Appl., 110, 295-321, 1999.

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems
42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions

Abstract: This paper contains two parts. In the first one we give a survey on sufficient and necessary conditions on a function $f$ to belong to the set of all pointwise multipliers of certain Lizorkin-Triebel spaces. In part two we use these results to investigate under which geometrical conditions on the boundary the characteristic function $\chi_E$ of an open set $E$ belongs to such a multiplier class.