A characterization of Besov-type spaces and applications to Hankel-type operators

Interpolating sequences on analytic Besov type spaces

“…The reproducing formula for B p (s) (see [5] or [22] for the case p = 2) gives maps B p (s) into and onto l p . The (pointwise) multipliers of B p (s) denoted by M (B p (s)) are those analytic functions g for which gf is in B p (s) whenever f is in B p (s).…”

“…There are several characterizations of Carleson measures for B p (s) (see [29] and [30] for a capacitary condition analogous to Stegenga's description in [25] of Carleson measures for B p , or [1] and [18] for non capacitary conditions), but for our purposes we only need the following simple observation proved in [5].…”

“…We also need the following result (see [5]) that says that Carleson measures for B p (s) are stable under the action of some integral operator.…”

Weak factorization and Hankel forms for weighted Bergman spaces on the unit ball

“…First of all, recall that the Bloch space is the dual of A 1 α under the integral pairing , α (see [24,Theorem 3.17]). We also need the following lemma, whose one dimensional analogue is essentially proved in [3]. Proof.…”

Carleson Measures, Riemann–Stieltjes and Multiplication Operators on a General Family of Function Spaces

“…Proof. If p > 1, the result follows from Lemma 2.1 of [8]. If 0 < p ≤ 1 we use the atomic decomposition for D p γ (see [30,Theorem 32]): there is a sequence {a k } in D and a sequence of numbers {λ k } ∈ ℓ p such that…”