Acta mathematica scientia, Series B >
AN IMPROVED HARDY´S INEQUALITY
Received date: 2011-09-30
Revised date: 2012-11-16
Online published: 2013-09-20
Supported by
The Permanent address of Assal MILOUD: Department of Mathematics, Higher Institute of Applied Mathematics and Informatics, University of Kairouan, 3100, Tunisia.
In this paper we shall extend Hardy´s inequality associated with Fourier trans-form to the strip n(2−p) ≤σ < n+p(N +1) where N = [n(1/p−1)], the greatest integer not exceeding n(1/p − 1).
Key words： Hardy´s space; Hardy´s inequality
Assal MILOUD , Rahmouni ATEF . AN IMPROVED HARDY´S INEQUALITY[J]. Acta mathematica scientia, Series B, 2013 , 33(5) : 1382 -1386 . DOI: 10.1016/S0252-9602(13)60089-2
[1] Assal M. Hardy´s type inequality associated with the Hankel transform for overcritical exponent. Integr Transf Spec F, 2010: 1–6
[2] Coifman R R. A real-variable characterization of Hp. Studia Math, 1974, 51: 269–274
[3] Fefferman C, Stein E M. Hp spaces of several variables. Acta Math, 1972, 129: 137–193
[4] Garcia-Cuerva J, Rubio de Francia J. Weighted Norm Inequalities and Related Topics. North Holland, 1985
[5] Kanjin Y. On Hardy-type inequalities and Hankel transforms. Monatshefte f¨ur Mathematik, 1999, 127: 311–319
[6] Stein E M. Harmonic Analysis, Real Variable Methods, Orthogonality and Oscillatory Integrals. Princeton, NJ: Princeton Univ Press, 1993
[7] Taibleson M H, Weiss G. The molecular characterization of certain Hardy spaces. Ast´erisque, 1980, 77: 67–149
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