𝒩(p, q, s)-type spaces in the unit ball of 𝑪n(I): basic properties and Hadamard gaps

Abstract

ABSTRACTThe purpose of this paper is to study a new class of function spaces, called -type spaces, in the unit ball of . We establish some basic properties of this new function space, together with a characterization via Green's function, and finally, we study the Hadamard gap series in -type spaces. This is the first paper in a five part series. The second paper deals with the Carleson measure, while the third paper deals with several different characterizations of -type spaces via various norms and some applications to distance problems. Moreover, the fourth paper deals with the atomic decomposition of those functions belonging to -type spaces, and finally, the fifth paper deals with the Riemann–Stieltjes operators and multipliers on -type spaces.