Off-Diagonal Two Weight Bumps for Fractional Sparse Operators

Rahm, Rob

doi:10.1007/s10476-023-0204-8

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2023

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“…In 2013, Lerner [22] proved this conjecture by assuming that

\bar{\Phi }\in B_p, \bar{\Psi }\in B_{p^{\prime }}

and a pair of weights

(\omega ,v)

satisfies

\begin{align*} \sup _Q\Vert \omega ^{1/p}\Vert _{\Psi ,Q}\Vert v^{-1/p}\Vert _{\Phi ,Q}&lt;\infty . \end{align*}

For two weight inequalities for other operators, see [7–9, 14, 20, 31, 34], etc. For more recent works on improving the bump conditions, see [25, 35, 37].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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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“…In 2013, Lerner [22] proved this conjecture by assuming that

\bar{\Phi }\in B_p, \bar{\Psi }\in B_{p^{\prime }}

and a pair of weights

(\omega ,v)

satisfies

\begin{align*} \sup _Q\Vert \omega ^{1/p}\Vert _{\Psi ,Q}\Vert v^{-1/p}\Vert _{\Phi ,Q}&lt;\infty . \end{align*}

For two weight inequalities for other operators, see [7–9, 14, 20, 31, 34], etc. For more recent works on improving the bump conditions, see [25, 35, 37].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%