INHOMOGENEOUS PLANCHEREL–PÔLYA INEQUALITIES ON SPACES OF HOMOGENEOUS TYPE AND THEIR APPLICATIONS.

In this paper, the authors establish the inhomogeneous Plancherel­Pôlya inequalities on spaces of homogeneous type by use of the inhomogeneous discrete Calderón reproducing formulas. As an application, the authors prove that the Lebesgue norms of the inhomogeneous Littlewood­Paley γ-function and S-function on spaces of homogeneous type are equivalent. All results are new even for Rn. [ABSTRACT FROM AUTHOR]