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• W3106023602 endingPage "113" @default.
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• W3106023602 abstract "The aim of this paper is to study the boundedness of different conical square functions that arise naturally from second order divergence form degenerate elliptic operators. More precisely, let $L_w=w^{-1},{rm div}(w,A,nabla)$ where $win A_2$ and $A$ is an $ntimes n$ bounded, complex-valued, uniformly elliptic matrix. D. Cruz-Uribe and C. Rios solved the $L^2(w)$-Kato square root problem obtaining that $sqrt{L_w}$ is equivalent to the gradient on $L^2(w)$. The same authors in collaboration with the second named author of this paper studied the $L^p(w)$-boundedness of operators that are naturally associated with $L_w$, such as the functional calculus, Riesz transforms, or vertical square functions. The theory developed admitted also weighted estimates (i.e., estimates in $L^p(v dw)$ for $vin A_infty(w)$), and in particular a class of degeneracy weights $w$ was found in such a way that the classical $L^2$-Kato problem can be solved. In this paper, continuing this line of research, and also that originated in some recent results by the second and third named authors of the current paper, we study the boundedness on $L^p(w)$ and on $L^p(v dw)$, with $vin A_infty(w)$, of the conical square functions that one can construct using the heat or Poisson semigroup associated with $L_w$. As a consequence of our methods, we find a class of degeneracy weights $w$ for which $L^2$-estimates for these conical square functions hold. This opens the door to the study of weighted and unweighted Hardy spaces and of boundary value problems associated with $L_w$." @default.
• W3106023602 created "2020-11-23" @default.
• W3106023602 creator A5003253341 @default.
• W3106023602 creator A5045898584 @default.
• W3106023602 creator A5076429692 @default.
• W3106023602 date "2017-12-08" @default.
• W3106023602 modified "2023-09-26" @default.
• W3106023602 title "Conical square functions for degenerate elliptic operators" @default.
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• W3106023602 doi "https://doi.org/10.1515/acv-2016-0062" @default.
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