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Restricted estimates of the fractional integral on the diagonal

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  • Ting Chen
  • Wenchang Sun

Abstract

For a function in a mixed‐norm Lebesgue space, we study the restriction of its fractional integral on the diagonal. We show that the restriction is weakly bounded when the indices satisfy certain conditions. We give a complete characterization of such indices. To prove this result, we generalize a classical result on operators that commute with translations.

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  • Ting Chen & Wenchang Sun, 2023. "Restricted estimates of the fractional integral on the diagonal," Mathematische Nachrichten, Wiley Blackwell, vol. 296(3), pages 1013-1024, March.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:3:p:1013-1024
    DOI: 10.1002/mana.202000529
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    References listed on IDEAS

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    1. J. Johnsen & S. Munch Hansen & W. Sickel, 2015. "Anisotropic Lizorkin–Triebel spaces with mixed norms — traces on smooth boundaries," Mathematische Nachrichten, Wiley Blackwell, vol. 288(11-12), pages 1327-1359, August.
    2. Rovshan A. Bandaliyev & Ayhan Serbetci & Sabir G. Hasanov, 2018. "On Hardy Inequality in Variable Lebesgue Spaces with Mixed Norm," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(4), pages 765-782, December.
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