TITLE:
Inequalities for Higher Order Riesz-Laguerre Transforms
AUTHORS:
Ammar Elobied, Abdelgader Siddig, Sabir Widatalla
KEYWORDS:
Riesz-Laguerre Transform, Polynomial Expansion, Weak-Type, Stein Complex Interpolation Theorem, Calderon-Zygmund-Type, Riesz-Gauss Transform
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.4,
April
26,
2022
ABSTRACT: The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a polynomial weight w that makes the Riesz-Laguerre transforms of order greater than or equal to 2 continuous from L1 (wdμα) into L1,∞ (dμα), under specific value α, where μα is the Laguerre measure.