Abstract
In this note we consider a certain class of convolution operators acting on the L p spaces of the one dimensional torus. We prove that the identity minus such an operator is nicely invertible on the subspace of functions with mean zero.
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Acknowledgements
This work was initiated while the authors were visiting the Weizmann Institute of Science in Rehovot, Israel. We thank Prof. Gideon Schechtman for supervision and making our stay possible.
We are grateful to Prof. Krzysztof Oleszkiewicz for his remarks which led to the present general statement of Theorem 2. We thank Prof. Keith Ball for helping us to simplify the proof of Lemma 2. We also appreciate all the valuable comments Prof. Stanisław Kwapień gave us.
Research of the First named author partially supported by NCN Grant no. 2011/01/N/ST1/ 01839. Research of the second named author partially supported by NCN Grant no. 2011/01/N/ST1/05960.
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Nayar, P., Tkocz, T. (2014). A Note on Certain Convolution Operators. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_26
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DOI: https://doi.org/10.1007/978-3-319-09477-9_26
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