Higher dimensional Hardy inequality

Drábek, Pavel; Heinig, H. P.; Kufner, Alois

doi:10.1007/978-3-0348-8942-1_1

Cited by 48 publications

(35 citation statements)

References 5 publications

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“…Conditions for the boundedness of P and Q on L p (w) analogous to M p and M p are proved in [4]. It is easy to check that all our results concerning N and S = P + Q can be carried out to the higher dimensional setting.…”

Section: Higher Dimensional Resultsmentioning

confidence: 93%

Calderon weights as Muckenhoupt weights

Zuazo¹,

Reyes²,

Ombrosi³

2013

Indiana Univ. Math. J.

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Abstract. The Calderón operator S is the sum of the the Hardy averaging operator and its adjoint. The weights w for which S is bounded on L p (w) are the Calderón weights of the class C p . We give a new characterization of the weights in C p by a single condition which allows us to see that C p is the class of Muckenhoupt weights associated to a maximal operator defined through a basis in (0, ∞). The same condition characterizes the weighted weaktype inequalities for 1 < p < ∞, but that the weights for the strong type and the weak type differ for p = 1. We also prove that the weights in C p do not behave like the usual A p weights with respect to some properties and, in particular, we answer an open question on extrapolation for Muckenhoupt bases without the openness property.

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Section: Higher Dimensional Resultsmentioning

confidence: 93%

Calderon weights as Muckenhoupt weights

Zuazo¹,

Reyes²,

Ombrosi³

2013

Indiana Univ. Math. J.

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“…These theorems could be directly deduced from results proved by P. Drabek, H. Heinig and A. Kufner (see Theorem 2.1, p. 4 and Theorem 2.3, p. 7 in [3]). …”

Section: Preliminariesmentioning

confidence: 88%

The Boundedness of High Order Riesz-Bessel Transformations Generated by the Generalized Shift Operator in Weighted L p,ω,γ -spaces with General Weights

Ekincioglu

2008

Acta Appl Math

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“…The best constant for (21), the case k > 1, is discussed in [1] and [4]. Inequalities (21) are mutually equivalent, since by writing one of them for 2 − k and |B(1)|…”

Section: B(r)| γ B(r)mentioning

confidence: 99%

“…and the constant Inequality (3) was improved by P. Drábek, H. P. Heinig and A. Kufner in [4], where an analogue of (1) …”

Section: Introductionmentioning

confidence: 99%

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Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls

Čižmešija

Pečarić

Perić

1999

Proc. Amer. Math. Soc.

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Abstract. Integral means of arbitrary order, with power weights and their companion means, where the integrals are taken over balls in R n centered at the origin, are introduced and related mixed-means inequalities are derived. These relations are then used in obtaining Hardy and Levin-Cochran-Lee inequalities and their companion results for n-dimensional balls. Finally, the best possible constants for these inequalities are obtained.

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Higher dimensional Hardy inequality

Cited by 48 publications

References 5 publications

Calderon weights as Muckenhoupt weights

Calderon weights as Muckenhoupt weights

The Boundedness of High Order Riesz-Bessel Transformations Generated by the Generalized Shift Operator in Weighted L p,ω,γ -spaces with General Weights

Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls

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