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The aim of this paper is to prove the weak type vector-valued inequality for the modified Hardy– Littlewood maximal operator for general Radon measure on ℝ  n  . Earlier, the strong type vector-valued inequality for the same operator and the weak type vector-valued inequality for the dyadic maximal operator were obtained. This paper will supplement these existing results by proving a weak type counterpart.

A Weak Type Vector-Valued Inequality for the Modified Hardy–Littlewood Maximal Operator for General Radon Measure on ℝ n