Sharp Logarithmic Inequalities for Two Hardy-type Operators

• Autorzy: Adam Osękowski
• Języki publikacji: EN

Abstrakty

EN

For any locally integrable f on ℝⁿ, we consider the operators S and T which average f over balls of radius |x| and center 0 and x, respectively:
$Sf(x) = 1/|B(0,|x|)| ∫_{B(0,|x|)} f(t)dt$, $Tf(x) = 1/|B(x,|x|)| ∫_{B(x,|x|)} f(t)dt$
for x ∈ ℝⁿ. The purpose of the paper is to establish sharp localized LlogL estimates for S and T. The proof rests on a corresponding one-weight estimate for a martingale maximal function, a result which is of independent interest.

Kategorie tematyczne

• 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 60G44: Martingales with continuous parameter

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: 63
• Numer: 3
• Strony: 237-247

Daty

wydano

2015

Twórcy

autor

Adam Osękowski

• Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba8039-12-2015