Hankel and Berezin Type Operators on Weighted Besov Spaces of Holomorphic Functions on Polydisks

摘要

Let S be the space of functions of regular variation and let omega = (omega (1),..., omega (n)), omega (j) a S. The weighted Besov space of holomorphic functions on polydisks, denoted by B (p) (omega) (0 p +a), is defined to be the class of all holomorphic functions f defined on the polydisk U (n) such that , where dm (2n)(z) is the 2ndimensional Lebesgue measure on U (n) and D stands for a special fractional derivative of f.We prove some theorems concerning boundedness of the generalized little Hankel and Berezin type operators on the spaces B (p) (omega) and L (p) (omega) (the weighted L (p) -space).