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Fractional integration, differentiation, and weighted Bergman spaces. (English) Zbl 0930.42007

Filling some gaps in the previous knowledge, the authors describe coefficient multipliers acting between certain weighted Bergman (or related) spaces. Also, in some cases criteria are found for a monotone or lacunary sequence to be the sequence of Taylor coefficients of a function in a given space among those mentioned above. There are some valuable technical innovations.
There is also a brief but informative survey of the earlier work.

MSC:

42B15 Multipliers for harmonic analysis in several variables
46E15 Banach spaces of continuous, differentiable or analytic functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
26A33 Fractional derivatives and integrals
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