On boundedness of Calderón-Toeplitz operators

Details On boundedness of Calderón-Toeplitz operators On boundedness of Calderón-Toeplitz operators

2011-02-17

arxiv.org/abs/1102.3710v2

Integr. Equ. Oper. Theory 70(4) (2011), 583-600

Mathematics

Functional Analysis

17 pages, v2: small changes after the referee's report and typos corrected

Scientific paper

10.1007/s00020-011-1883-2

We study the boundedness of Toeplitz-type operators defined in the context of the Calder\'on reproducing formula considering the specific wavelets whose Fourier transforms are related to Laguerre polynomials. Some sufficient conditions for simultaneous boundedness of these Calder\'on-Toeplitz operators on each wavelet subspace for unbounded symbols are given, where investigating the behavior of certain sequence of iterated integrals of symbols is helpful. A number of examples and counterexamples is given.

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