Paraproducts and Hankel operators of Schatten class via p-John-Nirenberg Theorem |
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Authors: | Sandra Pott Martin P Smith |
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Institution: | Department of Mathematics, Analysis Research Group, University of York, Heslington, York, England YO10 5DD, UK |
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Abstract: | We give an interpolation-free proof of the known fact that a dyadic paraproduct is of Schatten-von Neumann class Sp, if and only if its symbol is in the dyadic Besov space Bpd. Our main tools are a product formula for paraproducts and a “p-John-Nirenberg-Theorem” due to Rochberg and Semmes.We use the same technique to prove a corresponding result for dyadic paraproducts with operator symbols.Using an averaging technique by Petermichl, we retrieve Peller's characterizations of scalar and vector Hankel operators of Schatten-von Neumann class Sp for 1<p<∞. We then employ vector techniques to characterise little Hankel operators of Schatten-von Neumann class, answering a question by Bonami and Peloso.Furthermore, using a bilinear version of our product formula, we obtain characterizations for boundedness, compactness and Schatten class membership of products of dyadic paraproducts. |
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Keywords: | 47B35 47B10 |
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