The closure of Dirichlet spaces in the Bloch space

Abstract

If 0 < p < ∞ and α > −1, the space of Dirichlet type D p α consists of those functions f which are analytic in the unit disc D and have the property that f ′ belongs to the

Closure of Bergman and Dirichlet spaces in the Bloch norm

“…The question then arises of when C B (A p ω,n ∩ B) can be characterized in terms of a simpler condition such as that of Corollary 2 but involving the level set Ω n,ε (f ). The following result is a generalization of [11,Theorem 2] for doubling weights, and answers this question in the affirmative in certain cases.…”

“…Therefore our contribution consists of showing that (i) and (iii) are equivalent. This equivalence is the counterpart of [11,Theorem 7] for weighted Dirichlet spaces induced by doubling weights.…”

Multipliers and closures of Besov-type spaces in the Bloch space

“…For 1 < p < ∞, Monreal Galán and Nicolau in [24] characterized the closure in the Bloch norm of the space H p ∩ B. Galanopoulos, Monreal Galán and Pau [16] generalize [24] to 0 < p < ∞ later. Recently, Bao and G ö g üs [6] and Galanopoulos and Girela [15] have investigated the closures in B of B ∩ D p α for certain spaces of Dirichlet Type D p α . For more results on closures of analytic function spaces in the Bloch space, we refer to [28] and [29].…”

“…For more results on closures of analytic function spaces in the Bloch space, we refer to [28] and [29]. In this paper, we study the closures of the B p (ρ) spaces, generalizing the main results in [6] and [15]. Meanwhile, interpolating Blaschke products in C B (B ∩ B p (ρ)) as multipliers of B p (ρ) ∩ BMOA are also investigated.…”

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.…”