Regularity of discrete multisublinear fractional maximal functions

We investigate the regularity properties of discrete multisublinear fractional maximal operators, both in the centered and uncentered versions. We prove that these operators are bounded and continuous from ℓ1(ℤd) × ℓ1(ℤd) × · · · × ℓ1(ℤd) to BV(ℤd), where BV(ℤd) is the set of functions of bounded variation defined on ℤd. Moreover, two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given. As applications, we present the regularity properties for discrete fractional maximal operator, which are new even in the linear case.

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