Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$

İsmail Ekincioğlu; Esra Kaya; Şeyma Ekincioglu

doi:10.31801/cfsuasmas.673191

Research Article

Year 2020, Volume: 69 Issue: 1, 847 - 853, 30.06.2020

İsmail Ekincioğlu Esra Kaya Şeyma Ekincioglu

https://doi.org/10.31801/cfsuasmas.673191

Abstract

References

El Hamma, M. and Daher, R., Generalization of Titchmarsh's Theorem for the Bessel transform, Rom. J. Math. Comput. Sci. 2(2), (2012), 17--22.
Ekincioglu, I. and Ozkin, I. K., On high order Riesz transformations generated by a generalized shift operator, Tr. J. Math. 21 (1997), 51--60.
Ekincioglu, I. and Serbetci, A., On the singular integral operators generated by the generalized shift operator, Int. J. App. Math. 1 (1999), 29--38.
Kipriyanov, I. A., Singular Elliptic Boundary Value Problems, Nauka, Moscow, Russia, 1997.
Kipriyanov, I. A. and Lyakhov, L. N., Multipliers of the mixed Fourier-Bessel transform, Dokl. Akad. Nauk. 354(4), (1997), 449--451.
Kipriyanov, I. A. and Klyuchantsev, M. I., On Singular Integrals Generated by The Generalized Shift Operator, II. Sib. Mat. Zh. 11 (1970), 1060--1083.
Levitan, B. M., The Theory of Generalized Translation Operators, Nauka, Moscow, Russia, 1973.
Levitan, B. M., Bessel function expansions in series and Fourier integrals, Uspekhi Mat. Nauk 6. 42(2), (1951), 102--143.
Levitan, B. M., Expansion in Fourier series and integrals over Bessel functions, Uspekhi Mat. Nauk 6. 2 (1951), 102--143.
El Quadih, S., Daher, R. and El Hamma, M., Generalization of Titchmarsh's Theorem for the Generalized Fourier-Bessel Transform in the Space L_{α,n}², International Journal of Mathematical Modelling Computations 6(3), (2016), 253--260.
Trimèche, K., Transmutation operators and mean-periodic functions associated with differential operators, Math. Rep. 4(1), (1988), 1--282.
Younis, M. S., Fourier transforms of Dini-Lipschitz functions, Internat. J. Math. & Math. Sci. 9(2), (1986) 301--312.

Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$

Year 2020, Volume: 69 Issue: 1, 847 - 853, 30.06.2020

İsmail Ekincioğlu Esra Kaya Şeyma Ekincioglu

https://doi.org/10.31801/cfsuasmas.673191

Abstract

In this paper, we prove a generalization of Titchmarsh's theorem for the Laplace-Bessel differential operator in the space
$L_{p,\gamma}(\mathbb{R}^{n}_{+})$ for functions satisfying the $(\psi,p)$-Laplace-Bessel Lipschitz condition for $1

0 $.

Keywords

Laplace-Bessel differential operator, generalized shift operator, Laplace-Bessel Lipschitz function

References

El Hamma, M. and Daher, R., Generalization of Titchmarsh's Theorem for the Bessel transform, Rom. J. Math. Comput. Sci. 2(2), (2012), 17--22.
Ekincioglu, I. and Ozkin, I. K., On high order Riesz transformations generated by a generalized shift operator, Tr. J. Math. 21 (1997), 51--60.
Ekincioglu, I. and Serbetci, A., On the singular integral operators generated by the generalized shift operator, Int. J. App. Math. 1 (1999), 29--38.
Kipriyanov, I. A., Singular Elliptic Boundary Value Problems, Nauka, Moscow, Russia, 1997.
Kipriyanov, I. A. and Lyakhov, L. N., Multipliers of the mixed Fourier-Bessel transform, Dokl. Akad. Nauk. 354(4), (1997), 449--451.
Kipriyanov, I. A. and Klyuchantsev, M. I., On Singular Integrals Generated by The Generalized Shift Operator, II. Sib. Mat. Zh. 11 (1970), 1060--1083.
Levitan, B. M., The Theory of Generalized Translation Operators, Nauka, Moscow, Russia, 1973.
Levitan, B. M., Bessel function expansions in series and Fourier integrals, Uspekhi Mat. Nauk 6. 42(2), (1951), 102--143.
Levitan, B. M., Expansion in Fourier series and integrals over Bessel functions, Uspekhi Mat. Nauk 6. 2 (1951), 102--143.
El Quadih, S., Daher, R. and El Hamma, M., Generalization of Titchmarsh's Theorem for the Generalized Fourier-Bessel Transform in the Space L_{α,n}², International Journal of Mathematical Modelling Computations 6(3), (2016), 253--260.
Trimèche, K., Transmutation operators and mean-periodic functions associated with differential operators, Math. Rep. 4(1), (1988), 1--282.
Younis, M. S., Fourier transforms of Dini-Lipschitz functions, Internat. J. Math. & Math. Sci. 9(2), (1986) 301--312.

There are 12 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	İsmail Ekincioğlu 0000-0002-5636-1214 Esra Kaya 0000-0002-6971-0452 Şeyma Ekincioglu 0000-0001-6700-8232
Publication Date	June 30, 2020
Submission Date	January 10, 2020
Acceptance Date	March 6, 2020
Published in Issue	Year 2020 Volume: 69 Issue: 1

Cite

APA	Ekincioğlu, İ., Kaya, E., & Ekincioglu, Ş. (2020). Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 847-853. https://doi.org/10.31801/cfsuasmas.673191
AMA	Ekincioğlu İ, Kaya E, Ekincioglu Ş. Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):847-853. doi:10.31801/cfsuasmas.673191
Chicago	Ekincioğlu, İsmail, Esra Kaya, and Şeyma Ekincioglu. “Fourier-Bessel Transforms of Dini-Lipschitz Functions on Lebesgue Spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 847-53. https://doi.org/10.31801/cfsuasmas.673191.
EndNote	Ekincioğlu İ, Kaya E, Ekincioglu Ş (June 1, 2020) Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 847–853.
IEEE	İ. Ekincioğlu, E. Kaya, and Ş. Ekincioglu, “Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 847–853, 2020, doi: 10.31801/cfsuasmas.673191.
ISNAD	Ekincioğlu, İsmail et al. “Fourier-Bessel Transforms of Dini-Lipschitz Functions on Lebesgue Spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 847-853. https://doi.org/10.31801/cfsuasmas.673191.
JAMA	Ekincioğlu İ, Kaya E, Ekincioglu Ş. Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:847–853.
MLA	Ekincioğlu, İsmail et al. “Fourier-Bessel Transforms of Dini-Lipschitz Functions on Lebesgue Spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 847-53, doi:10.31801/cfsuasmas.673191.
Vancouver	Ekincioğlu İ, Kaya E, Ekincioglu Ş. Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):847-53.