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New estimates for the B-Riesz transform
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In this paper, we study the B-Riesz transformation R(k)? generated by a generalized translation operator Ty (y ? Rn+). We prove that the Cotlar-type inequality holds for these operators. In particular, we prove results related to the Cotlar inequality for the even and odd cases of the kernel of the B-Riesz transform. Thus, new estimates for the B-Riesz transform in weighted Lebesgue spaces Lp,?,w are obtained.
Title: New estimates for the B-Riesz transform
Description:
In this paper, we study the B-Riesz transformation R(k)? generated by a generalized translation operator Ty (y ? Rn+).
We prove that the Cotlar-type inequality holds for these operators.
In particular, we prove results related to the Cotlar inequality for the even and odd cases of the kernel of the B-Riesz transform.
Thus, new estimates for the B-Riesz transform in weighted Lebesgue spaces Lp,?,w are obtained.
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