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Abstract
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We study certain singular integral operators, as well as their corresponding truncated
maximal operators, along polynomial curves. Assuming that the kernels of operators
are rough not only on the unit sphere but also on the radial direction, we
establish certain weighted estimates for these operators. As applications, we
obtain that these operators are bounded on the mixed radial-angular spaces
and on the vector-valued mixed radial-angular spaces
. The
bounds are independent of the coefficients of the polynomials in the definition of the
operators. Our results we obtained improve theorems of Antonio Córdoba (2016)
and Piero D’Ancona and Renato Lucà (2016).
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Keywords
singular integral, maximal singular integral, rough kernel,
mixed radial-angular space, vector-valued mixed
radial-angular space, vector-valued norm inequality
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Mathematical Subject Classification 2010
Primary: 42B20
Secondary: 42B25
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Milestones
Received: 19 September 2017
Revised: 12 June 2018
Accepted: 26 June 2018
Published: 16 September 2019
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