In this paper, we prove a variant of a general Hardy-Knopp type inequality. We also formulate a convolution inequality in the language of topological groups. By our main results we obtain a general form of multidimensional strengthened Hardy and Pólya-Knopp-type inequalities.

We use some results from the theory of reproducing kernel Hilbert spaces to show that reachable space heat equation for a finite rod with either one or two Dirichlet boundary controls is RKHS analytic functions on square, and we compute its as an infinite double series. also null half line data sector, whose (essentially) sum pullbacks Bergman Hardy kernels plane \(\mathbb {C}^+\).

We give a generalization of the notion finite Blaschke products from perspective generalized inner functions in various reproducing kernel Hilbert spaces. Further, we study precisely how these relate to so-called Shapiro--Shields and shift-invariant subspaces generated by polynomials. Applying our results, show that only entire on weighted Hardy spaces over unit disk are multiples monomials, ex...