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

Erdoğan Şen^1, , 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

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 Z_p. 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 Z_p. Finally, we derive some interesting properties involving this-type maximal operator.

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

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