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RESEARCH PRODUCT

Multipliers on Vector Valued Bergman Spaces

José Luis ArreguiJosé Luis ArreguiOscar Blasco

subject

Pure mathematicsSequenceGeneral Mathematics010102 general mathematicsBanach spaceFunction (mathematics)Type (model theory)01 natural sciencesMultiplier (Fourier analysis)Bergman spaceBounded function0103 physical sciences010307 mathematical physics0101 mathematicsUnit (ring theory)Mathematics

description

AbstractLet X be a complex Banach space and let Bp(X) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y defines a multiplier between Bp(X) and Bq(Y) (resp. Bp(X) and lq(Y)) if for any function we have that belongs to Bq(Y) (resp. (Tn(xn))n ∈ lq(Y)). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in Bp(X) are introduced.

yearjournalcountryeditionlanguage
2002-12-01Canadian Journal of Mathematics
https://doi.org/10.4153/cjm-2002-044-3