Wyniki wyszukiwania

1

Local integrability of strong and iterated maximal functions

100%

Hagelstein P.

Studia Mathematica

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2001

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tom 147

|

nr 1

37-50

EN

Let $M_{S}$ denote the strong maximal operator. Let $M_{x}$ and $M_{y}$ denote the one-dimensional Hardy-Littlewood maximal operators in the horizontal and vertical directions in ℝ². A function h supported on the unit square Q = [0,1]×[0,1] is exhibited such that $∫_{Q} M_{y}M_{x}h < ∞$ but $∫_{Q} M_{x}M_{y}h = ∞$. It is shown that if f is a function supported on Q such that $∫_{Q} M_{y}M_{x}f < ∞$ but $∫_{Q} M_{x}M_{y}f = ∞$, then there exists a set A of finite measure in ℝ² such that $∫_{A} M_{S}f = ∞$.

2

On the uniqueness of the uncentered ergodic maximal function

100%

Hagelstein P.

Fundamenta Mathematicae

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2004

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tom 183

|

nr 1

81-90

EN

It is shown that if two functions share the same uncentered (two-sided) ergodic maximal function, then they are equal almost everywhere.

3

A note on rare maximal functions

100%

Hagelstein P.

Colloquium Mathematicum

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2003

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tom 95

|

nr 1

49-51

EN

A necessary and sufficient condition is given on the basis of a rare maximal function $M_{l}$ such that $M_{l}f ∈ L¹([0,1])$ implies f ∈ L log L([0,1]).

4

Orlicz bounds for operators of restricted weak type

100%

Hagelstein P.

Colloquium Mathematicum

|

2005

|

tom 103

|

nr 2

193-197

EN

It is shown that if T is a sublinear translation invariant operator of restricted weak type (1,1) acting on L¹(𝕋), then T maps simple functions in L log L(𝕋) boundedly into L¹(𝕋).

Ograniczanie wyników

2 Colloquium Mathematicum

1 Fundamenta Mathematicae

1 Studia Mathematica

4 Hagelstein P.

1 2005

1 2004

1 2003

1 2001

Local integrability of strong and iterated maximal functions

On the uniqueness of the uncentered ergodic maximal function

A note on rare maximal functions

Orlicz bounds for operators of restricted weak type