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A class of the Newtonian HK-Sobolev spaces on metric measure spaces

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Abstract

In this article, the authors present a systematic study of a class of the Newtonian HK-Sobolev spaces on metric measure spaces. Several Sobolev-type embeddings are discussed in the context of the Newtonian HK-Sobolev spaces. As an application, the boundedness of the fractional maximal operator on the Newtonian HK-Sobolev spaces is also investigated.

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Funding

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada

    H. M. Srivastava

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China

    H. M. Srivastava

  3. Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Republic of Korea

    H. M. Srivastava

  4. Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City, 320314, Taiwan, Republic of China

    H. M. Srivastava

  5. Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007, Baku, Azerbaijan

    H. M. Srivastava

  6. Section of Mathematics, International Telematic University Uninettuno, 00186, Rome, Italy

    H. M. Srivastava

  7. Department of Mathematics, Sipajhar College, Darrang, Sipajhar, Assam, 784145, India

    Parthapratim Saha

  8. Department of Mathematics, Gauhati University, Guwahati, Assam, 781014, India

    Bipan Hazarika

Authors
  1. H. M. Srivastava
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  2. Parthapratim Saha
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  3. Bipan Hazarika
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The authors contributed equally to the preparation of this article. All authors read and approved the final manuscript.

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Correspondence to H. M. Srivastava.

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Srivastava, H.M., Saha, P. & Hazarika, B. A class of the Newtonian HK-Sobolev spaces on metric measure spaces. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 84 (2024). https://doi.org/10.1007/s13398-024-01584-1

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  • DOI: https://doi.org/10.1007/s13398-024-01584-1

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