Extensions of the Calderón-Zygmund theory

• Autores: Bernat Ramis Vich
• Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 9, Nº. 1, 2024, págs. 11-20
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen
  • català

    Les eines desenvolupades en la dècada de 1950 per Calderón i Zygmund ens permeten demostrar que algunes integrals singulars estan ben definides i fitades en els espais Lp. Tot i que l’espai euclidià fos el context original on totes aquestes idees es varen desenvolupar, aquestes propietats es generalitzen a altres espais mètrics de mesura i a integrals singulars de valors vectorials. Al llarg de les dècades, la teoria ha anat guanyant en abstracció i interès. Encara avui en dia, hi ha operadors que s’escapen de l’abast de la teoria, com és l’operador diàdic esfèric maximal.

  • English

    The tools developed in the 1950s by Calder´on and Zygmund enable us to prove that certain singular integrals are well defined and bounded in Lp spaces. Although the Euclidean space was the original context where all these ideas were developed, these properties generalise to other measure metric spaces and to vector-valued singular integrals. Along the decades, the theory has been acquiring abstraction and luring attention. Even nowadays, there are operators that fall outside the scope of the theory, for instance the dyadic spherical maximal operator.

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