References
-
A. Achour and K. Trimeche, La g-fonction de Littlewood-Paley associee a un operateur differentiel singulier sur ]0;+
${\infty}$ [, Ann. Inst. Fourier, Grenoble, 33(1983), 203-226. https://doi.org/10.5802/aif.946 - B. Amri and L. T. Rachdi, The Littlewood-Paley g-function associated with the Riemann-Liouville operator, Ann. Univ. Paedagog. Crac. Stud. Math., 12(2013), 31-58.
- B. Amri and L. T. Rachdi, Uncertainty principle in terms of entropy for the Riemann-Liouville operator, Bull. Malays. Math. Sci. Soc., (Accepted papers).
- B. Amri and L. T. Rachdi, Beckner Logarithmic Uncertainty principle for the Riemann-Liouville operator, Internat. J. Math., 24(9)(2013), 1350070 (29 pages). https://doi.org/10.1142/S0129167X13500705
- B. Amri and L. T. Rachdi, Calderon-reproducing formula for singular partial differential operators, Integral Transforms Spec. Funct., 25(8)(2014), 597-611. https://doi.org/10.1080/10652469.2014.888807
-
H. Annabi and A. Fitouhi, La g-fonction de Littlewood-Paley associee a une classe d'operateurs differentiels sur ]0;+
${\infty}$ [ contenant l'operateur de Bessel, C. R. Acad. Sc. Paris, 303(1986), 411-413. - C. Baccar, N. B. Hamadi and L. T. Rachdi, Inversion formulas for the Riemann-Liouville transform and its dual associated with singular partial differential operators, Int. J. Math. Math. Sci., 2006(2006), pp 1-26.
- C. Baccar, N. B. Hamadi and L. T. Rachdi, An analogue of Hardy's theorem and its Lp-version for the Riemann-Liouville transform associated with singular partial differential operators, J. Math. Sci. (Dattapukur), 17(1)(2006), 1-18.
- N. B. Hamadi and L. T. Rachdi, Weyl Transforms Associated with the Riemann-Liouville Operator, Int. J. Math. Math. Sci., 2006, Article ID 94768, 1-18.
- C. Baccar, N. B. Hamadi and L. T. Rachdi, Best approximation for Weierstrass transform connected with Riemann-Liouville operator, Commun. Math. Anal., 5, No. 1, (2008) 65-83.
-
C. Baccar and L. T. Rachdi, Spaces of
$D_Lp$ type and a convolution product associated with the Riemann-Liouville operator, Bull. Math. Anal. Appl., Vol. 1, Iss., 3(2009), 16-41. - W. R. Bloom and H. Heyer, Harmonic analysis of probability measures on hypergroups, de Gruyter studies in mathematics 20, walter de Gruyter, Berlin-New York 1995.
- A. Erdelyi et al., Tables of integral transforms, Mc Graw-Hill Book Compagny., 2, New York 1954.
- A. Erdelyi., Asymptotic expansions, Dover publications, New-York 1956.
- J. A. Fawcett, Inversion of n-dimensional spherical averages, SIAM Journal on Applied Mathematics, 45(2)(1985), 336-341. https://doi.org/10.1137/0145018
- S. Helgason. The Radon Transform. Birkhauser, 2nd edition, 1999.
- H. Hellsten and L.-E. Andersson, An inverse method for the processing of synthetic aperture radar data, Inverse Problems, 3(1)(1987), 111-124. https://doi.org/10.1088/0266-5611/3/1/013
- M. Herberthson, A numerical implementation of an inverse formula for CARABAS raw data, Internal Report D30430-3.2, National Defense Research Institude, FOA, Box 1165; S-581 11, Linkoping, 1986.
- I. I. Hirschman, Jr., Variation diminishing Hankel transforms, J. Anal. Math., 8(1960/61), 307-336.
- Kh. Hleili, S. Omri and L. T. Rachdi, Uncertainty principle for the Riemann-Liouville operator, Cubo, 13(3)(2011), 91-115. https://doi.org/10.4067/S0719-06462011000300006
- N. N. Lebedev, Special Functions and Their Applications, Dover publications, New-York 1972.
-
S. Omri and L. T. Rachdi, An
$L^p$ -$L^q$ version of Morgan's theorem associated with Riemann-Liouville transform, Int. J. Math. Anal., 1(17)(2007), 805-824. - S. Omri and L. T. Rachdi, Heisenberg-Pauli-Weyl uncertainty principle for the Riemann-Liouville Operator, J. Inequal. Pure and Appl. Math., 9, Iss. 3, Art 88 (2008).
- L. T. Rachdi and A. Rouz, On the range of the Fourier transform connected with Riemann-Liouville operator, Ann. Math. Blaise Pascal, 16(2)(2009), 355-397. https://doi.org/10.5802/ambp.272
-
F. Soltani, Littlewood-Paley g-function in the Dunkl analysis on
${\mathbb{R}}^d$ , J. Ineq. Pure and Appl. Math. 6, Issue 3, (2005), Article 84, 13 pp. (electronic). - E. M. Stein, Interpolation of linear operator, Trans. Amer. Math. Soc., 83(2)(1956), 482-492. https://doi.org/10.1090/S0002-9947-1956-0082586-0
- E. M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory, Ann. of Math. Stud., Princeton Univ. Press, Princeton, New Jersey, 63, 1970.
- E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University, New Jersey 1971.
- K. Stempak, La theorie de Littlewood-Paley pour la transformation de Fourier-Bessel, C. R. Acad. Sc. Paris, Serie I, Math., 303(1986), 15-18.
- G. N. Watson, A treatise on the theory of Bessel functions, Cambridge univ. Press., 2nd ed., Cambridge 1959.