Boundary multipliers of a family of Möbius invariant function spaces

Abstract

Abstract. For 1 < p < ∞ and 0 < s < 1, we consider the function spaces Q p s (T) that appear naturally as the space of boundary values of a certain family of analytic Möbius invariant function spaces on the the unit disk. In this paper, we give a complete description of the pointwise multipliers going from Q p1 s (T) to Q p2 r (T) for all ranges of 1 < p 1 , p 2 < ∞ and 0 < s, r < 1. The spectra of such multiplication operators is also obtained.

A Note of the Interpolating Sequence in Qp∩H∞

“…We know in this paper that the space F( pp -2s) is a subspace of B by Corollary 2.8 of Ref. [15]. An analytic function f Î F( pp -2s) if and only if the positive mea-…”