Abstract
Given a real polynomial p(t) in one variable such that p(0) = 0, we consider the maximal operator in R 2 , M p f(x 1 , x 2 ) = sup |f(x 1 -2 i p (t), x 2 -2 j p (t))| dt. h>0, i,j∈Z We prove that Mp is bounded on L q (R 2 ) for q > 1 with bounds that only depend on the degree of p.
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