Department of Mathematics,
Birla Institute of Technology And Science- Pilani,
Hyderabad Campus, Jawahar Nagar, Kapra Mandal,
District.-Medchal-500 078, Telangana,
India.
E-mail: alphonse@hyderabad.bits-pilani.ac.in
p20180442@hyderabad.bits-pilani.ac.in
URL: https://www.bits-pilani.ac.in/hyderabad/a-michael-alphonse
https://www.bits-pilani.ac.in/research_scholars/sri-sakti-swarup-anupindi

Abstract:

In this paper, we prove strong type inequality for maximal commutator of singular operator on weighted lp spaces. Using these results we prove strong type inequality for the maximal commutator of singular operator on variable exponent sequence spaces. Using Calderon-Coifman-Weiss transference principle we prove strong type inequality for maximal ergodic commutator of singular operator on a probability space equipped with measure preserving transformation U.

Paper's Title:

Maximal Singular Operators On Variable Exponent Sequence Spaces and Their Corresponding Ergodic Version

Author(s):

Sri Sakti Swarup Anupindi and Michael A. Alphonse

Department of Mathematics, Birla Institute of Technology And Science- Pilani,
Hyderabad Campus, Jawahar Nagar, Kapra Mandal,
District.-Medchal-500 078 Telangana,
India.
E-mail: p20180442@hyderabad.bits-pilani.ac.in alphonse@hyderabad.bits-pilani.ac.in
URL: https://www.bits-pilani.ac.in/hyderabad/a-michael-alphonse
https://www.bits-pilani.ac.in/research_scholars/sri-sakti-swarup-anupindi

Abstract:

In this paper, we prove strong and weak type inequalities of singular operators on weighted l_w^p(Z)$. Using these results, we prove strong type and weak type inequalities of the maximal singular operator of Calderon-Zygmund type on variable exponent sequence spaces l^p(·)(Z). Using the Calderon-Coifman-Weiss transference principle, we prove strong type, weak type inequalities of the maximal ergodic singular operator on L_w^p(X,B,μ) spaces, where (X,B,μ) is a probability space equipped with measure preserving transformation U.

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