On Hilbert-type boundary-value problem of poly-Hardy class on the unit disc

Abstract

In this article, the poly-Hardy class on the unit disc is introduced and the boundary behaviour of the function in this class is discussed. Then the method used in Wang (Y.F. Wang, On modified Hilbert boundary-value problems of polyanalytic functions, Math. Methods Appl. Sci. 32 (2009), pp. 1415–1427) is applied to Hilbert-type boundary-value problems for the poly-Hardy class on the unit disc, and the expression of solution and the condition of solvability are explicitly obtained.