Given a real polynomial p(t) in one variable such that p(0) = 0, we consider the maximal operator in R2, Mpf(x1, x2)= sup h>0, i, jℤZ 1/h ∫ h0 |f(x1-2ip(t), x2-2jp(t))| dt. We prove that Mp is bounded on Lq(ℝ2) for q > 1 with bounds that only depend on the degree of p.
Maximal functions with polynomial densities in lacunary directions
RICCI, Fulvio
2003
Abstract
Given a real polynomial p(t) in one variable such that p(0) = 0, we consider the maximal operator in R2, Mpf(x1, x2)= sup h>0, i, jℤZ 1/h ∫ h0 |f(x1-2ip(t), x2-2jp(t))| dt. We prove that Mp is bounded on Lq(ℝ2) for q > 1 with bounds that only depend on the degree of p.File in questo prodotto:
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HareMaximal functions with polynomial densitiesTrans. Amer. Math. Soc.20031135-1144 (electronic)355.pdf
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