New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions

Martín-Reyes, F. J.

doi:10.1090/s0002-9939-1993-1111435-2

Cited by 69 publications

(65 citation statements)

References 6 publications

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“…In particular, the result holds if w belongs to the Sawyer's class [7] A~( 1+o) since A~( 1+a) c A~a. This inclusion follows from A~ C A~a, 1 < r < p(l +a), which is true by Holder's inequality and the implication w e A~( 1+a) =>• w 6 A~ for some r < p(\ + a) (see [7] or [6]). …”

Section: T;f (X) < C[m~f (X) + T*f (X)]mentioning

confidence: 87%

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Two weighted ineqalities for maximal functions related to Cesàro convergence

Bernardis¹,

Martín-Reyes²

2003

J. Aust. Math. Soc.

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Section: T;f (X) < C[m~f (X) + T*f (X)]mentioning

confidence: 87%

“…(ii) (u, v) A. L. Bernardis and F. J. Martin-Reyes [6] that N > 2 On the other hand, since the function…”

Section: Is Of Weak Type (P P) With Respect To U(x) DX and V(x)dxmentioning

confidence: 99%

Two weighted ineqalities for maximal functions related to Cesàro convergence

Bernardis¹,

Martín-Reyes²

2003

J. Aust. Math. Soc.

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“…Unfortunately, one-sided weights A + p do not satisfy the reverse Hölder inequality. However, a substitute was found in [24]:…”

Section: One-sided Estimates On Weighted Hardy Spacesmentioning

confidence: 99%

Some one-sided estimates for oscillatory singular integrals

Pan

et al. 2014

Nonlinear Analysis: Theory, Methods & Applications

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Abstract. The purpose of this paper is to establish some one-sided estimates for oscillatory singular integrals. The boundedness of certain oscillatory singular integral on weighted Hardy spaces H 1 + (w) is proved. It is here also show that the H 1 + (w) theory of oscillatory singular integrals above cannot be extended to the case of H q + (w) when 0 < q < 1 and w ∈ A + p , a wider weight class than the classical Muckenhoupt class. Furthermore, a criterion on the weighted L p -boundednesss of the oscillatory singular integral is given.

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“…In fact, from the results of [4,5], weights which do not belong to A p (B) still satisfy the inequality…”

Section: Introductionmentioning

confidence: 99%