Annali di Matematica Pura ed Applicata

, Volume 114, Issue 1, pp 87–102

# Multiplication properties of besov spaces

• Hans Triebel
Article

## Summary

The paper deals with the question whether f → gf (pointwise multiplication) is a bounded operator from B p,q s =B p,q s (Rn) into itself. Here B p,q s are the general (non-homogeneous isotropic) Besov spaces; −<s<∞; 0<p ≦∞; 0<q ≦. A special case of the main result (formulated in the theorem in3.1) is the following. If g is the characteristic function of a half-space, then f → gf is a bounded operator in B p,q s if
$$s \in \left\{ \begin{gathered} \left( {\frac{1}{p} - 1,\frac{1}{p}} \right)for 1 \leqq p \leqq \infty , \hfill \\ \left( {n\left( {\frac{1}{p} - 1} \right),\frac{1}{p}} \right)for\frac{{n - 1}}{n}< p \leqq 1, \hfill \\ \end{gathered} \right.$$
and it is not a bounded operator in B p,q s if either0<p<n −1 / n or
$$s \notin \left\{ \begin{gathered} \left[ {\frac{1}{p} - 1,\frac{1}{p}} \right]for 1 \leqq p \leqq \infty , \hfill \\ \left[ {n\left( {\frac{1}{p} - 1} \right),\frac{1}{p}} \right]for\frac{{n - 1}}{n}< p \leqq 1. \hfill \\ \end{gathered} \right.$$
(For1<p< these results are known). The paper is the continuation of.

## Keywords

Characteristic Function Multiplication Property Bounded Operator Besov Space Pointwise Multiplication
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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