Rosalio G. Artes Jr.
Department of Mathematics, College of Arts and 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 Street, Baku, AZ1096, Azerbaijan; International Center for Interdisciplinary Research in Sciences, The University of Lahore, Lahore 54792, Pakistan.
Mujahid Abbas
Department of Mechanical Engineering Science, Faculty of Engineering and the Built Environment, University of Johannesburg, Auckland Park, Johannesburg 2092, South Africa; Department of Medical Research, China Medical University, Taichung 406040, Taiwan.
Muhammad Tariq
Mathematics Research Center, Near East University, Near East Boulevard, Nicosia, Mersin, 99138, Turkey.
Mutum Zico Meetei
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia.
Abdelfatah Abasher
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia.
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, Szechenyl Istvan University, Egyetem ter 1, H-9026 Gyor, Hungary.
Abstract
We establish some new mapping properties of truncated Havin–Maz'ya potentials on complete noncompact Riemannian manifolds with nonnegative Ricci curvature. In contrast to earlier results based on the Herz-space framework used in the Euclidean theory, we employ the heat semigroup associated to the Laplace–Beltrami operator to define heat-semigroup Besov spaces, and construct a truncated potential from a prescribed Orlicz function. Under nonnegative Ricci curvature, this potential is bounded between the relevant Besov spaces if and only if the manifold satisfies Euclidean volume growth, while sub-Euclidean growth rules out any such boundedness; its gradient satisfies a weak-type endpoint estimate. We also present applications to regularity properties.