Abstract
The purpose of this paper is to establish an atomic decomposition for functions in the weighted mixed norm space \(A^{p,q}_\omega \) induced by a radial weight \(\omega \) in the unit disc admitting a two-sided doubling condition. The obtained decomposition is further applied to characterize Carleson measures for \(A^{p,q}_\omega \), and bounded differentiation operators \(D^{(n)}(f)=f^{(n)}\) acting from \(A^{p,q}_\omega \) to \(L^s_\mu \), induced by a positive Borel measure \(\mu \), on the full range of parameters \(0<p,q,s<\infty \).
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Acknowledgements
This research was supported in part by Ministerio de Economía y Competitivivad, Spain, Projects P6C2018-096166-B-100 and MTM2015-69323-REDT; La Junta de Andalucía, Project FQM210 and UMA18-FEDERJA-002; Academy of Finland Project No. 268009. Funding was provided by Espacios de funciones y operadores entre ellos (Grant No. MTM2014-51834-P).
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Peláez, J.Á., Rättyä, J. & Sierra, K. Atomic Decomposition and Carleson Measures for Weighted Mixed Norm Spaces. J Geom Anal 31, 715–747 (2021). https://doi.org/10.1007/s12220-019-00296-y
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DOI: https://doi.org/10.1007/s12220-019-00296-y