Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Go
Turkish Journal of Analysis and Number Theory. 2013, 1(1), 4-8
DOI: 10.12691/tjant-1-1-2
Open AccessResearch Article

q-Hardy-Littlewood-Type Maximal Operator with Weight Related to Fermionic p-Adic q-Integral on Zp

Erdoğan Şen1, , Mehmet Acikgoz2 and Serkan Araci3

1Department of Mathematics, Faculty of Science and Letters, Namik Kemal University, Tekirdağ, Turkey

2Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, Turkey

3Hatay, Turkey

Pub. Date: September 23, 2013
(This article belongs to the Special Issue Recent developments in the areas of mathematics)

Cite this paper:
Erdoğan Şen, Mehmet Acikgoz and Serkan Araci. q-Hardy-Littlewood-Type Maximal Operator with Weight Related to Fermionic p-Adic q-Integral on Zp. Turkish Journal of Analysis and Number Theory. 2013; 1(1):4-8. doi: 10.12691/tjant-1-1-2

Abstract

The q-extension of Hardy-littlewood-type maximal operator in accordance with q Volkenborn integral in the p-adic integer ring was recently studied . A generalization of Jang's results was given by Araci and Acikgoz . By the same motivation of their papers, we aim to give the definition of the weighted q-Hardy-littlewood-type maximal operator by means of fermionic p-adic q-invariant distribution on Zp. Finally, we derive some interesting properties involving this-type maximal operator.

Keywords:
fermionic p-adic q-integral on Zp hardy-littlewood theorem p-adic analysis q-analysis

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  S. Araci and M. Acikgoz, A note on the weighted q-Hardy-littlewood-type maximal operator with respect to q-Volkenborn integral in the -adic integer ring, J. Appl. Math. & Informatics, Vol. 31(2013), No. 3-4, pp. 365-372.
 
[2]  S. Araci, M. Acikgoz and E. Şen, On the extended Kim's p-adic q-deformed fermionic integrals in the p-adic integer ring, Journal of Number Theory 133 (2013) 3348-3361.
 
[3]  T. Kim, Lebesgue-Radon-Nikodym theorem with respect to fermionic -adic invariant measure on Zp, Russ. J. Math. Phys. 19 (2012).
 
[4]  T. Kim, Lebesgue-Radon-Nikodym theorem with respect to fermionic q-Volkenborn distribution on μp, Appl. Math. Comp. 187 (2007), 266-271.
 
[5]  T. Kim, S. D. Kim, D.W. Park, On Uniformly differntiabitity and q-Mahler expansion, Adv. Stud. Contemp. Math. 4 (2001), 35-41.
 
[6]  T. Kim, q-Volkenborn integration, Russian J. Math. Phys. 9 (2002) 288-299.
 
[7]  T. Kim, On a q-analogue of the p-adic log Gamma functions and related integrals, Journal of Number Theory 76 (1999), 320-329.
 
[8]  T. Kim, Note on Dedekind-type DC sums, Advanced Studies in Contemporary Mathematics 18(2) (2009), 249-260.
 
[9]  T. Kim, A note on the weighted Lebesgue-Radon-Nikodym Theorem with respect to p-adic invariant integral on Zp, J. Appl. Math. & Informatics, Vol. 30(2012), No. 1, 211-217.
 
[10]  T. Kim, Non-archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math Phys. 10 (2003) 91-98.
 
[11]  L-C. Jang, On the q-extension of the Hardy-littlewood-type maximal operator related to q -Volkenborn integral in the -adic integer ring, Journal of Chungcheon Mathematical Society, Vol. 23, No. 2, June 2010.
 
[12]  K. Hensel, Theorie der Algebraischen Zahlen I. Teubner, Leipzig, 1908.
 
[13]  N. Koblitz, p-adic Numbers, p-adic Analysis and Zeta Functions, Springer-Verlag, New York Inc, 1977.