Vertical square functions and other operators associated with an elliptic operator

Abstract: Although, in general, vertical and conical square functions are equivalent operators just in $L^2$, in this talk we show that, when this square functions are defined through the heat or Poisson semigroup that arise from an elliptic operator, there exist open intervals of p's containing 2 where the equivalence holds in $L^p$. As a consequence we obtain new boundedness results for some square functions. We also show how similar ideas lead us to improve the known range where a non-tangential maximal function associated with the Poisson semigroup is bounded.

analysis of PDEsclassical analysis and ODEsfunctional analysismetric geometry

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.