Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
Keyword(s):
Let X be a Banach function space over the unit circle T and let H[X] be the abstract Hardy space built upon X. If the Riesz projection P is bounded on X and a∈L∞, then the Toeplitz operator Taf=P(af) is bounded on H[X]. We extend well-known results by Brown and Halmos for X=L2 and show that, under certain assumptions on the space X, the Toeplitz operator Ta is bounded (resp., compact) if and only if a∈L∞ (resp., a=0). Moreover, aL∞≤TaB(H[X])≤PB(X)aL∞. These results are specified to the cases of abstract Hardy spaces built upon Lebesgue spaces with Muckenhoupt weights and Nakano spaces with radial oscillating weights.
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1996 ◽
Vol 144
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pp. 179-182
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2003 ◽
Vol 55
(2)
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pp. 379-400
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2018 ◽
Vol 61
(1)
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pp. 231-248
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1991 ◽
Vol s3-63
(3)
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pp. 595-619
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2015 ◽
Vol 67
(5)
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pp. 1161-1200
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