On new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in tubular domains over symmetric cones

Abstract

We introduce new multifunctional mixed norm analytic Herz-type spaces in tubular domains over symmetric cones and provide new sharp embedding theorems for them. Some results are new even in case of onefunctional holomorphic spaces. Some new related sharp results for new multifunctional Bergman-type spaces will be also provided under one condition on Bergman kernel.

Keywords

• bergman spaces
• herz spaces
• tubular domains over symmettic cones
• embedding theorems
• analytic functions
• аналитические функции
• трубчатая область
• пространство герца
• пространство бергмана
• теоремы вложения