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Compact Hankel operators on harmonic Bergman spaces

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Abstract

We study Hankel operators on the harmonic Bergman spaceb 2(B), whereB is the open unit ball inR n,n≥2. We show that iff is in\(C(\bar B)\) then the Hankel operator with symbolf is compact. For the proof we have to extend the definition of Hankel operators to the spacesb p(B), 1<p<∞, and use an interpolation theorem. We also use the explicit formula for the orthogonal projection ofL 2(B, dV) ontob 2(B). This result implies that the commutator and semi-commutator of Toeplitz operators with symbols in\(C(\bar B)\) are compact.

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References

  1. Sheldon Axler, Paul Bourdon, Wade Ramey,Harmonic Function Theory, Springer-Verlag, New York, 1992

    Google Scholar 

  2. A. Benedek, R. Panzone,The Spaces L p,with Mixed Norm, Duke Math. J. 28 (1961), 301–324

    Article  Google Scholar 

  3. Colin Bennett, Robert Sharpley,Interpolation of Operators, Academic Press, 1988

  4. Nelson Dunford, Jacob T. Schwartz,Linear Operators, Part I, Interscience Publishers, Inc., 1958

  5. Svante Janson, Thomas Wolff,Schatten classes and Commutators of Singular Integral Operators, Arkiv for Matematik 20 (1982), No.2, 301–310

    Google Scholar 

  6. Ewa Ligocka, Estimates in Sobolev Norms\(\parallel \cdot \parallel _p^s \) for Harmonic and Holomorphic Functions and Interpolation Between Sobolev and Hölder Spaces of Harmonic Functions, Studia Mathematica 86 (1987), 255–271

    Google Scholar 

  7. Ewa Ligocka,On the Reproducing Kernel for Harmonic Functions and the Space of Bloch Harmonic Functions on the Unit Ball in R n, Studia Mathematica 87 (1987), 23–32

    Google Scholar 

  8. Michael Reed, Barry Simon,Methods of Modern Mathematical Physics, Academic Press, 1972

  9. Bernard Russo,On the Hausdorff-Young Theorem for Integral Operators, Pacific Journal of Mathematics, Vol.68, No.1, 1977, 241–253

    Google Scholar 

  10. Bernard Russo,The Norm of the L p-Fourier Transform on Unimodular Groups, Transactions of the American Mathematical Society, Vol.192, 1974, 293–305

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, 48824, East Lansing, MI, USA

    Mirjana Jovović

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  1. Mirjana Jovović
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Jovović, M. Compact Hankel operators on harmonic Bergman spaces. Integr equ oper theory 22, 295–304 (1995). https://doi.org/10.1007/BF01378778

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