Análisis multilineal para operadores pseudodiferenciales periódicos y discretos en espacios Lp

  • Duván Cardona Pontificia Universidad Javeriana, Departmento de Matemáticas, Bogotá, Colombia.
  • Vishvesh Kumar Indian Institute of Technology Delhi, Department of Mathematics, New Delhi-110016, India.

Resumen

En esta nota anunciamos los resultados de nuestra investigación sobre las propiedades Lp de operadores pseudodiferenciales multilineales periódicos y/o discretos. Primero, revisaremos el análisis multilineal de tales operadores mostrando versiones análogas de los teoremas clásicos disponibles en el análisis multilineal euclidiano (debidos a Coifman y Meyer, Tomita, Miyachi, Fujita, Grafakos, Tao, etc.), pero, en el contexto de operadores periódicos y/o discretos. Se caracterizará la s-nuclearidad, 0 < s ≤ 1, para operadores multilineales pseudodiferenciales periódicos y/o discretos. Para cumplir este objetivo se clasificarán aquellos operadores lineales s-nucleares, 0 < s ≤ 1, multilineales con núcleo, sobre espacios de Lebesgue arbitrarios definidos en espacios de medida σ-finitos. Finalmente, como aplicación de los resultados presentados se obtiene la versión periódica de la desigualdad de Kato-Ponce, y se examina la s-nuclearidad de potenciales de Bessel lineales y multilineales, como también la s-nuclearidad de operadores integrales de Fourier periódicos admitiendo símbolos con tipos adecuados de singularidad.

Palabras clave: Operador pseudo-diferencial, operador discreto, operador periódico, nuclearidad, continuidad, operador integral de Fourier, Análisis multilineal

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Citas

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Publicado
2018-12-12