Estimates for Schur Multipliers and Double Operator Integrals—A Wavelet Approach

We discuss the work of Birman and Solomyak on singular numbers integral operators from point view modern approximation theory, in particular, with use wavelet techniques. are able to provide a simple proof norm estimates for kernel $$B^{1/p-1/2}_{p,p}(\mathbb R,L_2(\mathbb R))$$ . This recovers, extends, sheds new light theorem Solomyak. also these techniques Schur multiplier bounds double operator integrals bounded symbol $$B^{1/p-1/2}_{2p/(2-p),p}(\mathbb R,L_\infty(\mathbb , which extends Solomyak’s result symbols without compact domain.