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1

Some weighted norm inequalities for a one-sided version of $g*_{λ}$

100%

de Rosa L., Segovia C.

Studia Mathematica

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2006

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tom 176

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nr 1

21-36

EN

We study the boundedness of the one-sided operator $g⁺_{λ,φ}$ between the weighted spaces $L^{p}(M¯w)$ and $L^{p}(w)$ for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of $g⁺_{λ,φ}$. For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of $g⁺_{λ,φ}$ from $L^{p}((M¯)^{[p/2]+1} w)$ to $L^{p}(w)$, where $(M¯)^{k}$ denotes the operator M¯ iterated k times.

2

Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup

81%

Macías R., Segovia C., Torrea J.

Studia Mathematica

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2006

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tom 172

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nr 2

149-167

EN

We obtain weighted $L^{p}$ boundedness, with weights of the type $y^{δ}$, δ > -1, for the maximal operator of the heat semigroup associated to the Laguerre functions, ${ℒ_{k}^{α}}_{k}$, when the parameter α is greater than -1. It is proved that when -1 < α < 0, the maximal operator is of strong type (p,p) if p > 1 and 2(1+δ)/(2+α) < p < 2(1+δ)/(-α), and if α ≥ 0 it is of strong type for 1 < p ≤ ∞ and 2(1+δ)/(2+α) < p. The behavior at the end points of the intervals where there is strong type is studied in detail and sharp results about the existence or not of strong, weak or restricted types are given.

3

On the function $g^{*}_{λ}$ and the heat equation

60%

Segovia C., Wheeden R. L.

Studia Mathematica

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1970-1971

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tom 37

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nr 1

57-93

Ograniczanie wyników

3 Studia Mathematica

3 Segovia C.

1 Macías R.

1 Torrea J.

1 Wheeden R. L.

1 de Rosa L.

2 2006

1 1970

Some weighted norm inequalities for a one-sided version of $g*_{λ}$

Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup

On the function $g^{*}_{λ}$ and the heat equation