Weak-type estimate for a maximal function Sanjay Patel 42B20Newton diagramCalderon-Zygmund decompositionvan der Corput's lemma Let $ P(s,t) $ denote a real-valued polynomial of real variables $s$ and $t$. In this paper we show that the maximal function $\mathcal{M}$ defined by \[\mathcal{M}f(x) = \sup_{0 < h,k < 1} \frac{1}{hk} \left|\int_0^h \int_0^k f(x-P(s,t))\,{\mathrm d}s \,{\mathrm d}t \right|\] is weak-type 1-1 with a bound dependent on the coefficients of $P$. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2689 10.1512/iumj.2006.55.2689 en Indiana Univ. Math. J. 55 (2006) 341 - 368 state-of-the-art mathematics http://iumj.org/access/