Order Boundedness of Weighted Composition Operators Between Two Classes of Function Spaces

Qing Ze LIN

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 317-324.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 317-324. DOI: 10.12386/A2022sxxb0025

Order Boundedness of Weighted Composition Operators Between Two Classes of Function Spaces

  • Qing Ze LIN
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Abstract

In this paper, we first investigate the correspondence between order boundedness and Hilbert-Schmidt of weighted composition operators Wϕ,φ(f):=ϕf∘φ. Then, by resorting to the estimates of the norms of point evaluation functionals δz and derivative point evaluation functionals δz′ on weighted Dirichlet spaces Dβq(0<q<∞,−1<β<∞) and derivative Hardy spaces Sp(0<p<∞), the order boundedness of weighted composition operators Wϕ,φ between weighted Dirichlet spaces Dβq and derivative Hardy spaces Sp are completely characterized.

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weighted Dirichlet space / derivative Hardy space / weighted composition operator / order boundedness

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Qing Ze LIN. Order Boundedness of Weighted Composition Operators Between Two Classes of Function Spaces. Acta Mathematica Sinica, Chinese Series, 2022, 65(2): 317-324 https://doi.org/10.12386/A2022sxxb0025

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