Entropy Bumps and another sufficient condition for the two-weight boundedness of sparse operators

Rahm, Robert; Spencer, Scott

doi:10.1007/s11856-017-1613-9

Cited by 8 publications

(8 citation statements)

References 18 publications

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“…In the case p = 2 this result was obtained by S. Treil and A. Volberg [18] (who gave the name "entropy bumps" to the bumps appearing in this expression), and it was extended to any p > 1 by M. Lacey and S. Spencer [7] (see also [15]).…”

Section: Orlicz Bumpsmentioning

confidence: 61%

“…There are several different ways of "bumping", see [2,6,11] for the Orlicz bumps and [7,15,18] for the so-called entropy bumps; we recall them below, in Section 5.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent work by R. Rahm and S. Spencer [15], yet another bumps were introduced. Assume that ϕ p is a function that is decreasing on (0, 1) and increasing on (1, ∞) and such that…”

Section: Introductionmentioning

confidence: 99%

“…

We improve bump conditions for the two-weight boundedness of Calderón-Zygmund operators introduced recently by R. Rahm and S. Spencer [15].

…”

mentioning

confidence: 99%

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On separated bump conditions for Calderon-Zygmund operators

Lerner¹

2020

Preprint

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Section: Orlicz Bumpsmentioning

confidence: 61%

“…There are several different ways of "bumping", see [2,6,11] for the Orlicz bumps and [7,15,18] for the so-called entropy bumps; we recall them below, in Section 5.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent work by R. Rahm and S. Spencer [15], yet another bumps were introduced. Assume that ϕ p is a function that is decreasing on (0, 1) and increasing on (1, ∞) and such that…”

Section: Introductionmentioning

confidence: 99%

“…

We improve bump conditions for the two-weight boundedness of Calderón-Zygmund operators introduced recently by R. Rahm and S. Spencer [15].

…”

mentioning

confidence: 99%

See 2 more Smart Citations

On separated bump conditions for Calderon-Zygmund operators

Lerner¹

2020

Preprint

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“…Numerous other partial results and extensions of them to more general contexts have since been achieved regarding Conjecture 1.2, see for instance [1], [7], [15], [20]. The proofs of all these results rely on reducing the problem to establishing two-weight bounds for sparse operators, via domination of Calderón-Zygmund operators by sparse operators.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Two-weight estimates for sparse square functions and the separated bump conjecture

Kakaroumpas¹

2019

Preprint

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We show that two-weight L 2 bounds for sparse square functions, uniformly with respect to the sparseness constant of the underlying sparse family, and in both directions, do not imply a two-weight L 2 bound for the Hilbert transform. We present an explicit example, making use of the construction due to Reguera-Thiele from [18]. At the same time, we show that such two-weight bounds for sparse square functions do not imply both separated Orlicz bump conditions of the involved weights for p = 2 (and for Young functions satisfying an appropriate integrability condition). We rely on the domination of L log L bumps by Orlicz bumps (for Young functions satisfying an appropriate integrability condition) observed by . Contents 1. Introduction and main results 1 2. Overview of the paper 6 3. The Reguera-Thiele [18] construction 10 4. Two-weight estimates for generalized sparse operators 13 5. Investigating separated bump conditions 25 6. Appendix 33 References 35

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Weighted estimates for square functions associated with operators

Wen

Shen

Sun

2023

Mathematische Nachrichten

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Let L be a non‐negative self‐adjoint operator on . Suppose that the kernels of the analytic semigroup satisfy the upper bound related to a critical function ρ but without any assumptions of smooth conditions on spacial variables. In this paper, we consider the weighted inequalities for square functions associated with L, which include the vertical square functions, the conical square functions and the Littlewood–Paley g‐functions. A new bump condition related to the critical function is given for the two‐weighted boundedness of square functions associated with L. Besides, we also prove the weighted inequalities for square functions associated with L on weighted variable Lebesgue spaces with new classes of weights considered in [5]. As applications, our results can be applied to magnetic Schrödinger operator, Laguerre operators.

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Entropy Bumps and another sufficient condition for the two-weight boundedness of sparse operators

Cited by 8 publications

References 18 publications

On separated bump conditions for Calderon-Zygmund operators

On separated bump conditions for Calderon-Zygmund operators

Two-weight estimates for sparse square functions and the separated bump conjecture

Weighted estimates for square functions associated with operators

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