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• W2512582636 abstract "Let $X$ be a metric space with a doubling measure. Let $L$ be a nonnegative self-adjoint operator acting on $L^2(X)$, hence $L$ generates an analytic semigroup $e^{-tL}$. Assume that the kernels $p_t(x,y)$ of $e^{-tL}$ satisfy Gaussian upper bounds and Holder's continuity in $x$ but we do not require the semigroup to satisfy the preservation condition $e^{-tL}1 = 1$. In this article we aim to establish the exponential-square integrability of a function whose square function associated to an operator $L$ is bounded, and the proof is new even for the Laplace operator on the Euclidean spaces ${mathbb R^n}$. We then apply this result to obtain: (i) estimates of the norm on $L^p$ as $p$ becomes large for operators such as the square functions or spectral multipliers; (ii) weighted norm inequalities for the square functions; and (iii) eigenvalue estimates for Schrodinger operators on ${mathbb R}^n$ or Lipschitz domains of ${mathbb R}^n$." @default.
• W2512582636 created "2016-09-16" @default.
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• W2512582636 date "2016-09-06" @default.
• W2512582636 modified "2023-10-17" @default.
• W2512582636 title "Exponential-square integrability, weighted inequalities for the square functions associated to operators and applications" @default.
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• W2512582636 doi "https://doi.org/10.48550/arxiv.1609.01516" @default.
• W2512582636 hasPublicationYear "2016" @default.
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