Existence and boundedness of multilinear Littlewood–Paley operators on Campanato spaces

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In this paper, we established the boundedness of multilinear Littlewood–Paley operators on Campanato spaces, including the multilinear g-function, multilinear Lusin's area integral and multilinear Littlewood–Paley gλ⁎-function. We proved that if the above operators are finite for one point, then they are finite almost everywhere. Moreover, norm inequalities do hold for the above operators on the corresponding Campanato spaces.