Wavelet and Fourier Analytic Characterizations of Pointwise Multipliers of Besov Spaces Bp,ps(Rn</mml:…

For any p∈(0,1] and s∈R, the authors prove two types of characterizations of the pointwise multiplier space M(Bp,ps(Rn)) of the Besov space Bp,ps(Rn). 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 Bp,p,unifs,τ(Rn) via Haar wavelets in the critical index τ=1p−sn.