Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665726 | Advances in Mathematics | 2014 | 21 Pages |
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)
Authors
Komla Domelevo, Stefanie Petermichl,