Boundedness and compactness of Reimann–Liouville two-wavelet multipliers

Abstract

We introduce the notion of a Reimann–Liouville two-wavelet multiplier, and we give its trace formula as a bounded linear operator in the trace class from $$L^{2}(d\nu _{\alpha })$$ into $$L^{2}(d\nu _{\alpha })$$ in terms of the symbol and the two admissible wavelets. Next, we give results on the boundedness and compactness of Reimann–Liouville two-wavelet multipliers on $$L^{p}(d\nu _{\alpha })$$ , $$1 \le p \le \infty $$ .