New Poissona??Sch type inequalities and their applications in quantum calculus

摘要

The Poisson type inequalities, which were improved by Shu, Chen, and Vargas-De-Te?3n (J.??Inequal. Appl. 2017:114, 2017), are generalized by using Poisson identities involving modified Poisson kernel functions with respect to a cone. New generalizations of improved Poissona??Sch type inequalities are obtained by using the generalized Montgomery identity associated with the Schr??dinger operator. As applications in quantum calculus, we estimate the size of weighted Schr??dingerean harmonic Bergman functions in the upper half space.