Fractional integration, differentiation, and weighted Bergman spaces

Abstract

We study the action of fractional differentiation and integration on weighted Bergman spaces and also the Taylor coefficients of functions in certain subclasses of these spaces. We then derive several criteria for the multipliers between such spaces, complementing and extending various recent results. Univalent Bergman functions are also considered.

Special Toeplitz operators on strongly pseudoconvex domains

“…Recall that a sequence {λ k } is of bounded variation if . But this contradicts Theorem 1.3 of [3]. This contradiction proves the Claim above.…”

“…We also mention the paper [19] which contains related, precursor results to those in [3]. In Theorem 1.3, part (a), of [3], it is shown that the sequence {k …”

“…To prove the sharpness of our Theorem 1.2, part (i), we will use some results from [3]. We also mention the paper [19] which contains related, precursor results to those in [3].…”

Spaces of analytic functions of Hardy-Bloch type

“…This is a particular case of Theorem 2.1 of [6] and follows from the work of Flett [12,13]. In view of this result and (1.2), it is natural to ask whether the inclusion B(p, 2) ⊂ A 2p (0 < p < ∞) holds.…”

Boundary behaviour of analytic functions in spaces of Dirichlet type

“…Let p and α be as in the statement and f (z) = ∞ n=0 a n z n ∈ Ᏸ So using [6, Lemma 1.1] (see also [12, part (iii) of Theorem 5]) and [6,Corollary 3.5], we deduce that the fractional integral…”