Continuous algorithms in adaptive sampling recovery

We study optimal algorithms in adaptive continuous sampling recovery of smooth functions defined on the unit d-cube Id≔[0,1]d. Functions to be recovered are in Besov space Bp,θα. The recovery error is measured in the quasi-norm ‖⋅‖q of Lq≔Lq(Id),0d/p, we prove the asymptotic order νn(Bp,θα,Lq)≍n−α/d.