Quantitative estimates for square functions with new class of weights
The main aim of this paper is to prove several quantitative weighted estimates for square functions associated with operators satisfying certain upper bounds corresponding to a new class of weights related to critical functions. The paper is based on the operator \(L\), which is a nonnegative self-adjoint operator on \(L^2(X)\), where \(X\) is a metric space with a doubling measure. Examples of the operator \(L\) which satisfies Theorem 1.2 (the main result of the paper) include: Laguerre operators on \(\left(\mathbb{R}^n, \prod_{i=1}^n x_i^{\alpha_i} d x_i\right)\) with \(\alpha_i>-1\) for each \(i\) and Schrödinger operators on noncompact Riemannian manifolds.
scientific article; zbMATH DE number 7622260
scientific article