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Decomposition of analytic measures on groups and measure spaces

100%

Asmar N., Montgomery-Smith S.

Studia Mathematica

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2001

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tom 146

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nr 3

261-284

EN

We consider an arbitrary locally compact abelian group G, with an ordered dual group Γ, acting on a space of measures. Under suitable conditions, we define the notion of analytic measures using the representation of G and the order on Γ. Our goal is to study analytic measures by applying a new transference principle for subspaces of measures, along with results from probability and Littlewood-Paley theory. As a consequence, we derive new properties of analytic measures as well as extensions of previous work of Helson and Lowdenslager, de Leeuw and Glicksberg, and Forelli.

2

Littlewood-Paley theory on solenoids

100%

Asmar N., Montgomery-Smith S.

Colloquium Mathematicum

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1993

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tom 65

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nr 1

69-82

3

A sharp estimate for the Hardy-Littlewood maximal function

81%

Grafakos L., Montgomery-Smith S., Motrunich O.

Studia Mathematica

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1999

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tom 134

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nr 1

57-67

EN

The best constant in the usual $L^p$ norm inequality for the centered Hardy-Littlewood maximal function on $ℝ^1$ is obtained for the class of all "peak-shaped" functions. A function on the line is called peak-shaped if it is positive and convex except at one point. The techniques we use include variational methods.

Ograniczanie wyników

2 Studia Mathematica

1 Colloquium Mathematicum

3 Montgomery-Smith S.

2 Asmar N.

1 Grafakos L.

1 Motrunich O.

1 2001

1 1999

1 1993

Decomposition of analytic measures on groups and measure spaces

Littlewood-Paley theory on solenoids

A sharp estimate for the Hardy-Littlewood maximal function