Affiliation:
1. Tekirdağ Namık Kemal Üniversitesi, Matematik Bölümü, Tekirdağ, Turkey
Abstract
We provide a full characterization in terms of the six parameters involved
the boundedness of all standard weighted integral operators induced by
harmonic Bergman-Besov kernels acting between different Lebesgue classes
with standard weights on the unit ball of Rn. These operators in some sense
generalize the harmonic Bergman-Besov projections. To obtain the necessity
conditions, we use a technique that heavily depends on the precise inclusion
relations between harmonic Bergman-Besov and weighted Bloch spaces on the
unit ball. This fruitful technique is new. It has been used first with
holomorphic Bergman-Besov kernels by Kaptano?lu and ?reyen. Methods of
the sufficiency proofs we employ are Schur tests or H?lder or Minkowski
type inequalities which also make use of estimates of Forelli-Rudin type
integrals.
Publisher
National Library of Serbia
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