On the regularity of maximal operators supported by submanifolds

Abstract We prove that the maximal operators supported by submanifolds are bounded and continuous on the Triebel–Lizorkin spaces F s p , q ( R d ) and Besov spaces B s p , q ( R d ) for 0 s 1 and 1 p , q ∞ . As a corollary, we also show that these operators are bounded and continuous on the fractional Sobolev spaces W s , p ( R d ) for 0 ≤ s 1 and 1 p ∞ . Our main results represent significant improvements as well as natural extensions of what was known previously.

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