Article ID Journal Published Year Pages File Type
4665726 Advances in Mathematics 2014 21 Pages PDF
Abstract

We show that multipliers of second order Riesz transforms on products of discrete abelian groups enjoy the LpLp estimate p⁎−1p⁎−1, where p⁎=max{p,q}p⁎=max{p,q} and p and q   are conjugate exponents. This estimate is sharp if one considers all multipliers of the form ∑iσiRiRi⁎ with |σi|⩽1|σi|⩽1 and infinite groups. In the real valued case, we obtain better sharp estimates for some specific multipliers, such as ∑iσiRiRi⁎ with 0⩽σi⩽10⩽σi⩽1. These are the first known precise LpLp estimates for discrete Calderón–Zygmund operators.

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Physical Sciences and Engineering Mathematics Mathematics (General)
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