LAUSR

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 $$L^{2}(d\nu _{\alpha })$$L2(dνα) into $$L^{2}(d\nu _{\alpha })$$L2(dνα) 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 $$L^{p}(d\nu _{\alpha })$$Lp(dνα), $$1 \le p \le \infty $$1≤p≤∞.