Fractional Medians and Their Maximal Functions
Copyright policy )Fractional Medians and Their Maximal Functions
In this article, we introduce the fractional medians, give an expression of the set of all fractional medians in terms of non-increasing rearrangements and then investigate mapping properties of the fractional maximal operators defined by such medians. The maximal operator is a generalization of that in Stromberg. It turns out that our maximal operator is a more smooth operator than the usual fractional maximal operator. Further, we give another proof of the embedding from $BV$ to $L^{n/(n-1),1}$ due to Alvino by using the usual medians.
accepted in J. Geom. Anal
- Kyoto University Japan
Maximal functions, Littlewood-Paley theory, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 42B02, 46E30, 46E35, fractional maximal operator, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, fractional medians, non-increasing rearrangements, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Maximal functions, Littlewood-Paley theory, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 42B02, 46E30, 46E35, fractional maximal operator, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, fractional medians, non-increasing rearrangements, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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