Wolff Potential and Birkhoff's Ergodic Theorem in Grand Variable Herz Spaces

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Published: 2026-07-20
DOI: https://doi.org/10.56947/51vxdc48
Keywords:
Wolff potential, grand variable Herz spaces, grand Lebesgue spaces, variable exponent, boundedness of fractional operators, ergodic theorem

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Rosalio G. Artes Jr.
Department of Mathematics, College of Mathematical Sciences, Mindanao State University – Tawi-Tawi College of Technology and Oceanography, 7500 Bongao, Tawi-Tawi, Philippines.
Waqar Afzal
Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan.; Center for Theoretical Physics, Khazar University, 41 Mehseti Str., Baku, AZ1096, Azerbaijan.
Samra Asjad
Department of Mathematics, The University of Alabama at Birmingham, Birmingham, AL, USA.
Muhammad Tariq
Mathematics Research Center, Near East University, Near East Boulevard, Nicosia, Mersin, 99138, Turkey.
Hijaz Ahmad
Irfan Suat Gunsel Operational Research Institute, Near East University, Nicosia/TRNC, Mersin 10, 99138, Turkey.; Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea.; Sustainability Competence Centre, Szeschenyi Istvesn University, Egyetem tesr 1, H-9026 Gyesr, Hungary.; VIZJA University, Okopowa 59, 01-043 Warsaw, Poland.

Abstract

In this article, we establish the boundedness of the Wolff potential operator and Birkhoff's ergodic theorem in grand variable Herz spaces. These concepts were previously studied in the setting of Lebesgue spaces. Our results extend and refine the existing literature by considering a more general functional framework, thereby providing broader applicability and sharper estimates than the previously known results.

Article Details

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Vol. 23 No. 2 (2026)

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Articles

How to Cite

Wolff Potential and Birkhoff’s Ergodic Theorem in Grand Variable Herz Spaces. (2026). Gulf Journal of Mathematics, 23(2). https://doi.org/10.56947/51vxdc48