Change of Variable Results for A p -and Reverse Holder RH r -Classes

Johnson, Raymond; Neugebauer, C. J.

doi:10.2307/2001798

Cited by 30 publications

(24 citation statements)

References 6 publications

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“…The condition q p < ∞ demands p < p + for the value of p + appearing in (7.3). The equivalence with powers of weights in the corresponding A p classes is mentioned in [1] and was obtained by R. Johnson and C. Neugebauer in [18]. It reads , as stated in [1].…”

Section: Proofmentioning

confidence: 94%

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Extrapolation of weights revisited: New proofs and sharp bounds

Duoandikoetxea

2011

Journal of Functional Analysis

112

105

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We use an appropriate factorization of the A p weights to give another proof of the extrapolation theorem of Rubio de Francia. It provides sharp bounds in terms of the A p -constant of the weights. Then we extend the result to more general settings including off-diagonal and partial range extrapolation. Among the applications, we prove by iteration a multivariable extrapolation theorem and give a sharp bound for Calderón-Zygmund operators on L p (w) for weights in A q (q < p).

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Section: Proofmentioning

confidence: 94%

“…In Section 7 we consider another version of the extrapolation theorem, the limited-range extrapolation considered in [1] (and also to some extent in [10] and [18]). …”

Section: A Weight Is a Nonnegative Locally Integrable Function A Weimentioning

confidence: 99%

Extrapolation of weights revisited: New proofs and sharp bounds

Duoandikoetxea

2011

Journal of Functional Analysis

112

105

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“…By the weighted weak -boundedness of (see Theorem 1.2), we have Since w is in the class , we get by Lemma 2.1(ii). Moreover, since when , then we apply the condition (2.8) of θ and inequality (2.1) to obtain As for the term , it follows directly from Chebyshev’s inequality and the pointwise estimate (3.1) that Moreover, by applying Hölder’s inequality and then the reverse Hölder inequality in succession, we can show that if and only if (see [18]), where denotes the reverse Hölder class. Another application of condition on w shows that In addition, note that .…”

Section: Proofs Of Theorems 21 and 22mentioning

confidence: 99%

Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces

Wang

2017

J Inequal Appl

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In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutators formed by b and are established. Also we study related problems about two-weight, weak type inequalities for and in the Morrey-type spaces and give partial results.

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“…In the proof of Theorem we there will be used the following lemma on properties of Muckenhoupt class