Open AccessBoundedness of the Maximal Function of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure and consequences
Author(s) -
Jorge Moreno,
Ebner Pineda,
Wilfredo Urbina Romero
Publication year - 2021
Publication title -
revista colombiana de matemáticas/revista colombiana de matematicas
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.176
H-Index - 7
eISSN - 2357-4100
pISSN - 0034-7426
DOI - 10.15446/recolma.v55n1.99097
Subject(s) - mathematics , semigroup , ornstein–uhlenbeck process , hermite polynomials , measure (data warehouse) , gaussian , gaussian measure , lp space , lebesgue measure , maximal function , pure mathematics , function (biology) , lebesgue's number lemma , discrete mathematics , mathematical analysis , lebesgue integration , banach space , stochastic process , statistics , riemann integral , physics , quantum mechanics , database , evolutionary biology , biology , computer science , operator theory , fourier integral operator
The main result of this paper is the proof of the boundedness of the Maximal Function T* of the Ornstein-Uhlenbeck semigroup {Tt}t≥ 0 in Rd, on Gaussian variable Lebesgue spaces Lp(.) (γd); under a condition of regularity on p(.) following [5] and [8]. As an immediate consequence of that result, the Lp(.) (γd)-boundedness of the Ornstein-Uhlenbeck semigroup {Tt}t≥ 0 in Rd is obtained. Another consequence of that result is the Lp(.) (γd)-boundedness of the Poisson-Hermite semigroup and the Lp(.) (γd)- boundedness of the Gaussian Bessel potentials of order β > 0.