Regularity of the Fractional Maximal Function

By Juha Kinnunen, Eero Saksman. 2003

149 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/79400460582a3d0fbb0535435b08ee870698f0e7

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Citations in the corpus

On the endpoint regularity of discrete maximal operators (2013, unknown): “This paradigm that an L-bound implies a W -bound was later extended to a local version of the maximal operator [9], to a fractional version [10] and to a multilinear version [5].”
Corrigendum to “On a discrete version of Tanaka’s theorem for maximal functions” (2010, background): “rted in 1998 by Kinunnen [9] that studies the regularity of maximal operators acting on Sobolev functions. Since then, many authors have contributed to extend the theory, for instance [4], [5], [10], [11], [12], always having in the background the general principle that, for maximal operators, an Lp”
On the variation of maximal operators of convolution type (2013, background): “The paradigm that an L-bound implies a W -bound was later extended to a local version of M in [10], to a fractional version in [11] and to a multilinear version in [5].”
On the regularity of maximal operators (2008, background): “1,p(Ω), p > 1, where Ω is a proper open subset of Rn ([5]), and the continuity of the maximal operator for W1,p(Rn), p > 1 ([8]). Other interesting papers related to this topic are [1], [3] and [6]. In the ﬁrst part of this paper we will be concerned with the following family of bilinear maxim”
On approximate differentiability of the maximal function (2010, background): “Let us also mention that the result of Kinnunen [10] has been applied and generalized by many authors ([2], [3], [6], [7], [8], [11], [12], [14], [15], [16], [17], [18], [20], [21], [25]).”
On the variation of the Hardy-Littlewood maximal function (2012, methodology): “The regularity of the fractional maximal function was studied by J. Kinnunen and E. Saksman [11].”
ON BOUNDEDNESS OF MAXIMAL FUNCTIONS IN SOBOLEV SPACES (2004, methodology): “Hence we conclude from Theorem 1 that (2) S : W 1;p(Rn) ! W 1;p(Rn) is bounded for n=(n 1) 10 ].”
Derivative bounds for fractional maximal functions (2015, methodology): “In [13], Kinnunen and Saksman studied the regularity properties of such fractional maximal operators.”