We will prove local and global Besov-type characterisations for the Bloch space and the little Bloch space. As a special case we obtain that the Bloch space consists of those analytic functions on the unit disc whose restrictions to pseudo-hyperbolic discs (of fixed pseudo-hyperbolic radius) uniformly belong to the Besov space. We also generalise the results to Bloch functions and little Bloch functions on the unit ball in C m . Finally we discuss the related spaces BMOA and VMOA.
Abstract. In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline.
We will discuss invertibility of Toeplitz products T f T % g g ; for analytic f and g; on the Bergman space and the Hardy space. We will furthermore describe when these Toeplitz products are Fredholm. # 2002 Elsevier Science (USA)
The Bourgain algebra of H°°(Ώ) relative to L°°(B) is shown to be H°°(B) + C(l) + V, where V is an ideal of functions in L°°(ID)) which vanish in an appropriate sense near the boundary of ID).
We consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products T f Tḡ are bounded on the weighted Bergman spaces. We prove results analogous to those we obtained in the setting of the unit disk and the polydisk.
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