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Small Hankel operator induced by measurable symbol acting on weighted Bergman spaces
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abstract
The boundedness of the small Hankel operator $h^\omega_{f}(g)=\overline{P_\omega}(fg)$ induced by a measurable symbol $f$ and the Bergman projection $P_\omega$ associated to a radial weight $\omega$ acting from the weighted Bergman space $A^p_\omega$ to its conjugate analytic counterpart $\overline{A^p_\omega}$ is characterized on the range $1<p<\infty$ when $\omega$ belongs to the class $\mathcal{D}$ of radial weights admitting certain two-sided doubling conditions. On the way to the proof a sharp integral estimate for certain modified Bergman kernels is obtained.
Forward citations
Cited by 2 Pith papers
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Optimal off-diagonal upper estimates for Bergman reproducing kernels
For radial weights on the unit disc, a sharp off-diagonal Bergman kernel estimate is equivalent to the one-sided moment-doubling condition, with new consequences for maximal functions and Carleson measures.
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Fractional Volterra-type operator induced by radial weight acting on Hardy space
A family of fractional Volterra operators parameterized by radial doubling weights is bounded (compact) on Hardy spaces iff the symbol is in BMOA (VMOA), and Schatten membership is governed by an integral condition on...
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