Non-tangential maximal functions and conical square functions with\n respect to the Gaussian measure

2010/03/22 by Jan Maas, Maas, Jan, Jan van Neerven +3
Economics, Econometrics and Finance · Mathematics · #42B25 #42B30 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1003.4092

openalex publication_date 2010/03/22 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

We study, in L¹( Rⁿ;\γ) with respect to the gaussian measure,\nnon-tangential maximal functions and conical square functions associated with\nthe Ornstein-Uhlenbeck operator by developing a set of techniques which allow\nus, to some extent, to compensate for the non-doubling character of the\ngaussian measure. The main result asserts that conical square functions can be\ncontrolled in L¹-norm by non-tangential maximal functions. Along the way we\nprove a change of aperture result for the latter. This complements recent\nresults on gaussian Hardy spaces due to Mauceri and Meda.\n

Citations

• Some new function spaces and their applications to Harmonic analysis
• Hp spaces of several variables

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