Backward Shift Operators on Bergman-Besov Spaces as Bergman Projections
Hakkı Turgay KaptanoğluWe express backward shift operators on all Bergman-Besov spaces in terms of Bergman projections in one and several variables including the Banach function spaces and the special Hilbert spaces such as Drury-Arveson and Dirichlet spaces. These operators are adjoints of the shift operators and their definitions for the case 𝑝 = 1 and proper Besov spaces require the use of nontrivial imbeddings of the spaces into Lebesgue classes. Our results indicate that the backward shifts are compositions of imbeddings into Lebesgue classes followed by multiplication operators by the conjugates of the coordinate variables followed by Bergman projections on appropriate spaces. We apply our results to the wandering subspace property of invariant subspaces of the shift operators on certain of our Hilbert spaces.