A note on fractional type integrals associated to operators

• Wen, Yongming ^[1] ; Hou, Xianming ^[2] ; Zhang, Jing ^[3]
  1. [1] Zhangzhou Normal University

     Zhangzhou Normal University

     China

     
  2. [2] Linyi University

     Linyi University

     China

     
  3. [3] Yili Normal University

     Yili Normal University

     China

     

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 1, 2026, págs. 133-148
• Idioma: inglés
• DOI: 10.1007/s13348-024-00461-9
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let \mathcal {L} be a non-negative self-adjoint operator on L^2(\mathbb {R}^d) and let e^{-t\mathcal {L}} be a semigroup generated by -\mathcal {L}. Assume that the kernels of e^{-t\mathcal {L}} satisfy the upper bound related to a critical radius function but do not possess any regularity conditions on spacial variables. We consider the class of A_{p,q} weights associated to critical radius function, denoted by A_{p,q}^{\rho }(\mathbb {R}^d), which include the classical Muckenhoupt A_{p,q}(\mathbb {R}^d) weights. We obtain the quantitative A_{p,q}^{\rho }(\mathbb {R}^d) estimates for fractional integrals associated to \mathcal {L}. Particularly, the quantitative weighted endpoint bound for fractional integrals associated to \mathcal {L} is first established, which was missing in the literature of Li, Rahm and Wick (Math Z 293(1-2): 259-283, 2019) . Moreover, we generalize weighted endpoint inequalities to weighted mixed weak type inequalities for fractional type integrals associated to \mathcal {L}. As applications, our results can be applied to settings of magnetic Schrödinger operator, Laguerre operators, etc.

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