Weighted estimates for bilinear fractional integral operators: a necessary and sufficient condition for power weights

• Autores: Yasuo Komori-Furuya
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 1, 2020, págs. 25-37
• Idioma: inglés
• DOI: 10.1007/s13348-019-00246-5
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• Resumen

  • We consider weighted estimates for two bilinear fractional integral operators ?2,? and ???. Moen (Collect Math 60:213–238, 2009) obtained a necessary and sufficient condition for ?2,?. However we know only some sufficient conditions for ??? which is a variant of the bilinear Hilbert transform. Restricted to power weights we obtain a necessary and sufficient condition for ???. We also prove a bilinear Stein–Weiss inequality.