Wyniki wyszukiwania

1

Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1

100%

Colzani L., Sjögren P.

Studia Mathematica

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1999

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tom 132

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nr 2

101-124

EN

We study convolution operators bounded on the non-normable Lorentz spaces $L^{1,q}$ of the real line and the torus. Here 0 < q < 1. On the real line, such an operator is given by convolution with a discrete measure, but on the torus a convolutor can also be an integrable function. We then give some necessary and some sufficient conditions for a measure or a function to be a convolutor on $L^{1,q}$. In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals, we give a necessary and sufficient condition. This condition is, however, only sufficient in the general case.

2

Eigenfunctions of the Hardy-Littlewood maximal operator

100%

Colzani L., Pérez Lázaro J.

Colloquium Mathematicum

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2010

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tom 118

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nr 2

379-389

EN

We prove that peak shaped eigenfunctions of the one-dimensional uncentered Hardy-Littlewood maximal operator are symmetric and homogeneous. This implies that the norms of the maximal operator on L(p) spaces are not attained.

3

Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces

100%

Brandolini L., Colzani L.

Colloquium Mathematicum

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1996

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tom 71

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nr 2

273-286

4

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Hardy-Lorentz spaces and expansions in eigenfunctions of the Laplace-Beltrami operator on compact manifolds

100%

Colzani L., Travaglini G.

Colloquium Mathematicum

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1989-1990

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tom 58

|

nr 2

305-315

5

Pointwise convergence of Fourier series on compact Lie groups

81%

Colzani L., Giulini S., Travaglini G., Vignati M.

Colloquium Mathematicum

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1990

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tom 60-61

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nr 2

379-386

6

From restricted type to strong type estimates on quasi-Banach rearrangement invariant spaces

81%

Carro M., Colzani L., Sinnamon G.

Studia Mathematica

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2007

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tom 182

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nr 1

1-27

EN

Let X be a quasi-Banach rearrangement invariant space and let T be an (ε,δ)-atomic operator for which a restricted type estimate of the form $∥Tχ_{E}∥_{X} ≤ D(|E|)$ for some positive function D and every measurable set E is known. We show that this estimate can be extended to the set of all positive functions f ∈ L¹ such that $||f||_{∞} ≤ 1$, in the sense that $∥Tf∥_{X} ≤ D(||f||₁)$. This inequality allows us to obtain strong type estimates for T on several classes of spaces as soon as some information about the galb of the space X is known. In this paper we consider the case of weighted Lorentz spaces $X = Λ^{q}(w)$ and their weak version.

7

Hankel transform on Lorentz spaces

50%

Colzani L.

Colloquium Mathematicum

|

1990

|

tom 60-61

|

nr 1

71-76

Ograniczanie wyników

5 Colloquium Mathematicum

2 Studia Mathematica

7 Colzani L.

2 Travaglini G.

1 Brandolini L.

1 Carro M.

1 Giulini S.

1 Pérez Lázaro J.

1 Sinnamon G.

1 Sjögren P.

1 Vignati M.

1 2010

1 2007

1 1999

1 1996

3 1990

Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1

Eigenfunctions of the Hardy-Littlewood maximal operator

Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces

Hardy-Lorentz spaces and expansions in eigenfunctions of the Laplace-Beltrami operator on compact manifolds

Pointwise convergence of Fourier series on compact Lie groups

From restricted type to strong type estimates on quasi-Banach rearrangement invariant spaces

Hankel transform on Lorentz spaces