Wavelet and Fourier analytic characterizations of pointwise multipliers of Besov spaces Bp,ps(Rn) with 0 < p ≤ 1

Abstract

For any $p\in (0,1]$ and $s\in R$, the authors prove two types of characterizations of the pointwise multiplier space $M\left(B_{p,p}^s\right(R^n\left)\right)$ of the Besov space $B_{p,p}^s\left(R^n\right)$. One type is based on wavelet analysis and is an extension of a well-known argument of Yves Meyer. The other type works with Fourier analytic terms. As an application of the above two types of characterizations, the authors further obtain a characterization of bounded functions in the uniform space $B_{p,p,\mathrm{unif}}^{s,\tau }\left(R^n\right)$ via Haar wavelets in the critical index $\tau =\frac{1}{p}-\frac{s}{n}$.