Summary
It is shown that certain convolution operators, including the Hilbert transform in the one dimensional case, leave invariant the Lp,λ spaces studied by Campanato, Stampacchia and others.
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Peetre, J. On convolution operators leavingL p,λ spaces invariant. Annali di Matematica 72, 295–304 (1966). https://doi.org/10.1007/BF02414340
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DOI: https://doi.org/10.1007/BF02414340