## Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions.(English)Zbl 1036.46024

Let $$B^s_{pq} (\mathbb{R}^n)$$ with $$1 \leq p,q \leq \infty$$ and $$s \in \mathbb{R}$$ be the well-known Besov spaces in Euclidean $$n$$-space $$\mathbb{R}^n$$. A function $$m \in L_\infty (\mathbb{R}^n)$$ is said to be a pointwise multiplier for $$B^s_{pq} (\mathbb{R}^n)$$ if $$f \mapsto mf$$ is a bounded map in $$B^s_{pq} (\mathbb{R}^n)$$. The characterisation of the collection of all pointwise multipliers, denoted by $$M(B^s_{pq})$$, has attracted a lot of attention for decades. The present paper deals with the characterisations of $$M(B^0_{\infty, \infty})$$ (Theorem 4) and $$M(B^0_{\infty, 1} )$$ (Theorem 5) which are especially complicated. Applications to regularity assertions for elliptic partial differential equations are given.

### MSC:

 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 35J15 Second-order elliptic equations

### Keywords:

Besov spaces; pointwise multipliers
Full Text:

### References:

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