Buckley, Stephen M.; Koskela, Pekka; Vukotić, Dragan Fractional integration, differentiation, and weighted Bergman spaces. (English) Zbl 0930.42007 Math. Proc. Camb. Philos. Soc. 126, No. 2, 369-385 (1999). 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. Reviewer: S.V.Kislyakov (St.Peterburg) Cited in 1 ReviewCited in 33 Documents 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 Keywords:multiplier; Taylor coefficients; lacunary sequence PDFBibTeX XMLCite \textit{S. M. Buckley} et al., Math. Proc. Camb. Philos. Soc. 126, No. 2, 369--385 (1999; Zbl 0930.42007) Full Text: DOI