Distances from Bloch Functions to Q K -Type Spaces

Abstract

We establish several formulas for distances from Bloch functions to some QK -type spaces, which generalize similar results of distances from Bloch functions to BM OA by Peter Jones, and to some Möbius invariant spaces by Ruhan Zhao.

Composition Operators and the Closure of Morrey Space in the Bloch Space

“…Conversely, suppose that (23) holds. Fix > 0 and let satisfy (23). Without loss of generality, we may assume that (0) = 0.…”

“…Bao and Gögüş [21] studied the closure of Dirichlet type spaces D (−1 < ≤ 1) in the Bloch space. See [22][23][24][25][26] for some related results.…”

Univalent functions in Dirichlet-type spaces

“…where ϕ a (z) = a−z 1−az . For more informations about Q K spaces, we refer to [4], [9], [10] and [14]. Corollary 1.…”

“…If K satisfies (1.2), we get K(2t) ≈ K(t) for t > 0 and we can assume that K is differentiable up to any desired order. For more informations about weighted function K, we refer to [4], [5], [9], [10], [14] and [31].…”

Product of composition and differentiation operators and closures of weighted Bergman spaces in Bloch type spaces

“…Bao and Göğüş in [4] characterized the closure of D 2 α ∩ B (-1 < α ≤ 1) in the Bloch space, where D 2 α is the Dirichlet type space. See [9,11,20,26,27,29] for more results of the closure of some function spaces in the Bloch space.…”