On generalized Hardy spaces associated with singular partial differential operators
- Amal Ghandouri amal.ghandouri@fst.utm.tn
- Hatem Mejjaoli mejjaoli.hatem@yahoo.fr
- Slim Omri slim.omri@fst.utm.tn
Downloads
DOI:
https://doi.org/10.56754/0719-0646.2502.289Abstract
We define and study the Hardy spaces associated with singular partial differential operators. Also, a characterization by mean of atomic decomposition is investigated.
Keywords
Mathematics Subject Classification:
B. Amri, “The Hardy-Littlewood operator associated with the Riemann-Liouville transform”, Indag. Math. (N.S.), vol. 29, no. 5, pp. 1270–1289, 2018. doi: 10.1016/j.indag.2018.05.007
B. Amri and L. Rachdi, “The Littlewood-Paley g-function associated with the Riemann- Liouville operator”, Ann. Univ. Paedagog. Crac. Stud. Math., vol. 12, pp. 31–58, 2013.
C. Baccar, N. Ben Hamadi, and L. Rachdi, “Best approximation for Weierstrass transform connected with Riemann-Liouville operator”, Commun. Math. Anal., vol. 5, no. 1, pp. 65–83, 2008.
C. Baccar, N. Ben Hamadi and S. Omri, “Fourier multipliers associated with singular partial differential operators”, Oper. Matrices, vol. 11, no. 1, pp. 37–53, 2017. doi: 10.7153/oam-11-03
C. Baccar, N. Ben Hamadi and L. T. Rachdi, “Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators”, Int. J. Math. Math. Sci., vol. 2006, Art. ID 086238, 2006. doi: 10.1155/IJMMS/2006/86238
C. Baccar and L. T. Rachdi, “Spaces of DLp-type and a convolution product associated with the Riemann-Liouville operators”, Bull. Math. Anal. Appl., vol. 1, no. 3, pp. 16–41, 2009.
N. Ben Hamadi and L. T. Rachdi, “Weyl transforms associated with the Riemann-Liouville operator”. Int. J. Math. Math. Sci., vol. 2006, Art. ID 094768, 2006. doi: 10.1155/IJMMS/2006/94768
R. Coifman and G. Weiss, “Extensions of Hardy spaces and their use in analysis”, Bull. Amer. Math. Soc., vol. 83, no. 4, pp. 569–645, 1977. doi: 10.1090/S0002-9904-1977-14325-5
J. A. Fawcett, “Inversion of n-dimensional spherical averages”, SIAM J. Appl. Math., vol. 45, no. 2, pp. 336–341, 1985. doi: 10.1137/0145018
C. Fefferman and E. N. Stein, “Hp spaces of several variables”, Acta Math., vol. 129, no. 3-4, pp. 137–193, 1972. doi: 10.1007/BF02392215
H. Helesten and L. E. Anderson, “An inverse method for the processing of synthetic aper- ture radar data”, Inverse Problems, vol. 3, no. 1, pp. 111–124, 1987. doi: 10.1088/0266- 5611/3/1/013
M. Herberthson, “A numerical implementation of an inverse formula for CARABAS raw Data”. Internal Report D 30430-3.2. National Defense Research Institute, FOA, Box 1165; S-581 11, Sweden, 1986.
K. Hleili, S. Omri and L. T. Rachdi, “Uncertainty principle for the Riemann-Liouville operator”, Cubo, vol. 13, no. 3, pp. 91–115, 2011. doi: 10.4067/s0719-06462011000300006
N. N. Lebedev, Special Functions and Their Applications. New York, USA: Dover Publications, Inc., 1972.
H. Mejjaoli and S. Omri, “Boundedness and compactness of Reimann-Liouville two- wavelet multipliers”, J. Pseudo-Differ. Oper. Appl., vol. 9, no. 2, pp. 189–213, 2018. doi: 10.1007/s11868-018-0235-2
S. Omri and L. T. Rachdi, “An Lp-Lq version of Morgan’s theorem associated with Riemann-Liouville transform”, Int. J. Math. Anal. (Ruse), vol. 1, no. 17-20, pp. 805–824, 2007.
S. Omri and L. T. Rachdi, “Heisenberg-Pauli-Weyl uncertainty principle for the Riemann-Liouville Operator”, JIPAM. J. Inequal. Pure Appl. Math., vol. 9, no. 3, Art. ID 88, 2008.
L. T. Rachdi and A. Rouz, “On the range of the Fourier transform connected with Riemann-Liouville operator”, Ann. Math. Blaise Pascal, vol. 16, no. 2, pp. 355–397, 2009. doi: 10.5802/ambp.272
A. Uchiyama, “A maximal function characterization of Hp on the space of homogeneous type”, Trans. Amer. Math. Soc., vol. 262, no. 2, pp. 579–592, 1980. doi: 10.2307/1999848
A. Uchiyama, Hardy Spaces on the Euclidean Space, Springer Monographs in Mathematics, Tokyo, Japan: Springer-Verlag, 2001. doi: 10.1007/978-4-431-67905-9
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Mathematical Li- brary, Cambridge, UK: Cambridge University Press, 1995.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 A. Ghandouri et al.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.