Anisotropic classes of inhomogeneous pseudodifferential symbols

• Autores: Arpad Bényi, Marcin Bownik
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 64, Fasc. 2, 2013, págs. 155-173
• Idioma: inglés
• DOI: 10.1007/s13348-011-0056-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class {S^{m}_{\gamma, \delta}} of inhomogeneous symbols. We extend a well-known L 2-boundedness result to the anisotropic class {S_{\delta, \delta}^0(A)}, 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class {S^0_{1,0}(A)} are bounded on L p spaces, 1 < p < ∞.

• Referencias bibliográficas
  • Bényi Á., Bownik M.: Anisotropic classes of homogeneous pseudodifferential symbols. Studia Math. 200, 41–66 (2010)
  • Bownik M.: Anisotropic Hardy spaces and wavelets. Memoirs of the American Mathematical Society 164(781), (2003)
  • Bownik M.: Atomic and molecular decompositions of anisotropic Besov spaces. Math. Z. 250, 539–571 (2005)
  • Bownik M., Ho K.-P.: Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces. Trans. Am. Math. Soc. 358, 1469–1510 (2006)
  • Calderón A.P., Vaillancourt R.: A class of bounded pseudo-differential operators. Proc. Natl. Acad. Sci. USA 69, 1185–1187 (1972)
  • Coifman, R.R., Meyer, Y.: Au delá des opérateurs pseudo-différentiels. Astérisque 57 (1978)
  • Cordes H.O.: On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators. J. Funct....
  • Fefferman C.: L p bounds for pseudo-differential operators. Isr. J. Math. 14, 413–417 (1973)
  • Garello G.: Anisotropic pseudodifferential operators of type 1,1. Ann. Mat. Pura Appl. IV, 135–160 (1998)
  • Grafakos L., Torres R.H.: Pseudodifferential operators with homogeneous symbols. Mich. Math. J. 46, 261–269 (1999)
  • Hörmander L.: On the L 2 continuity of pseudo-differential operators. Commun. Pure Appl. Math. 24, 529–535 (1971)
  • Journé, J.L.: Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón. In: Lecture Notes in Mathematics,...
  • Kumano-go H.: A problem of Nirenberg on pseudo-differential operators. Commun. Pure Appl. Math. 23, 115–121 (1970)
  • Leopold H.-G.: Boundedness of anisotropic pseudo-differential operators in function spaces of Besov-Hardy-Sobolev type. Z. Anal. Anwendungen...
  • Miyachi A.: Estimates for pseudodifferential operators with exotic symbols. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34, 81–110 (1987)
  • Stein, E.M.: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press (1993)