A class of Integral Operators from Lebesgue spaces into Harmonic Bergman-Besov or Weighted Bloch Spaces

2020/05/10 by Doğan, Ömer Faruk
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2005.05314

Abstract

We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of ℝⁿ and characterize precisely those that are bounded from Lebesgue spaces L^p_α into Harmonic Bergman-Besov b^q_β or weighted Bloch Spaces b^∞_β , for 1≤ p≤∞, 1≤ q< ∞ and α,β∈ ℝ. These operators can be viewed as generalizations of the harmonic Bergman-Besov projections. Also, our results remove the disturbing conditions β>-1 when q

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