We characterize Carleson measures for weighted harmonic mixed norm spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2024_1654_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">$B^{p,q}_\alpha (\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>B</mi> <mi>α</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of harmonic functions on smoothly bounded domains in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2024_1654_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb {R}^n$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> for a certain range of parameters p, q and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2024_1654_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>. This result extends earlier characterization obtained by the second author to a wider range of parameters. Also, we characterize vanishing Carleson measures for these spaces and apply these results to obtain criteria for boundedness and compactness of Toeplitz operators on weighted mixed norm spaces.

Carleson Measures for Weighted Harmonic Mixed-Norm Spaces and Toeplitz Operators

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发表日期：

2025年1月5日

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Miloš Arsenović,
Ivana Savković

摘要

We characterize Carleson measures for weighted harmonic mixed norm spaces $B^{p,q}_\alpha (\Omega )$ $B_{α}^{p, q} (Ω)$ of harmonic functions on smoothly bounded domains in $\mathbb {R}^n$ $R^{n}$ for a certain range of parameters p, q and $\alpha $ $α$ . This result extends earlier characterization obtained by the second author to a wider range of parameters. Also, we characterize vanishing Carleson measures for these spaces and apply these results to obtain criteria for boundedness and compactness of Toeplitz operators on weighted mixed norm spaces.