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We introduce p-quasilocal operators and prove that if a sublinear operator T is p-quasilocal and bounded from to then it is also bounded from the classical Hardy space $H_p(T)$ to (0 < p ≤ 1). As an application it is shown that the maximal operator of the one-parameter Cesàro means of a distribution is bounded from $H_p(T)$ to (3/4 < p ≤ ∞) and is of weak type $(L_1,L_1)$. We...
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