Embedding Bergman spaces into tent spaces

2015/04/13 by Peláez, José Ángel, Rättyä, Jouni, Sierra, Kian · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1504.03091

Abstract

Let A^p_ω denote the Bergman space in the unit disc \mathbbD of the complex plane induced by a radial weight ω with the doubling property ∫_r¹ω(s) ds≤ C∫_(1+r)/(2)¹ω(s) ds. The tent space T^q_s(ν,ω) consists of functions such that \beginequation* \beginsplit ‖f‖_T^qs(ν,ω)^q =∫_\mathbbD(∫_Γ(ζ)|f(z)|^s dν(z))^\fracqsω(ζ) dA(ζ) 0, by considering a generalized area operator. The results are provided in terms of Carleson measures for A^p_ω.

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