Abstract
After proving a result of continuity for pseudo-differential operators whose symbols belong to Hölder spaces and satisfy a decay of quasihomogeneous type, the authors construct a suitable symbolic calculus and a parametrrx for quasi-elliptic operators; these tools are applied to the study of quasi-elliptic linear partial differential equations with H:older coefficients.
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References
C. Feffermann, L p bounds for pseudo-differential operators, Israel J. Math. 14 (1973), 413–417.
G. Garello, Pseudodifferential operators with symbols in weighted Sobolev spaces and regularity for non linear partial differential equations, Math. Nachr. 239–240 (2002), 62–79.
G. Garello and A. Morando, Lp-bounded pseudodifferential operators and regularity for multi-quasi-elliptic equations, Integral Equations Operator Theory 51 (2005), 501–517.
G. Garello and A. Morando, L p boundedness for pseudodifferential operators with non smooth symbols and applications, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 8(8) (2005), 461–503.
G. Garello and A. Morando, Continuity in quasi-homogeneous Sobolev spaces for pseudo-differential operators with Besov symbols, in Modern Trends in Pseudo-Differential Operators, Editors: J. Toft, M.W. Wong and H. Zhu, Operator Theory: Advances and Applications 172, Birkhäuser, 2007, 161–172.
R. Lascar, Propagation des singularités des solutions d’équations pseudodifférentielles quasi-homogènes, Ann. Inst. Fourier Grenoble 27 (1977), 79–123.
P.I. Lizorkin, (L p , L q )-multipliers of Fourier integrals, Dokl. Akad. Nauk SSSR 152 (1963), 808–811.
J. Marschall, Pseudo-differential operators with coefficients in Sobolev spaces, Trans. Amer. Math. Soc. 307(1) (1988), 335–361.
E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series 30, Princeton University Press, Princeton, N.J., 1970.
M.E. Taylor, Pseudodifferential Operators and Nonlinear PDF, Birkhäuser, Boston, Basel, Berlin, 1991.
M.E. Taylor, Tools for PDF: Pseudodifferential Operators, Paradifferential Operators and Layer Potentials, American Mathematical Society, 2000.
H. Triebel, Theory of Function Spaces, Birkhäuser Verlag, Basel, Boston, Stuttgart, 1983.
M.W. Wong, An Introduction to Pseudo-Differential Operators, Second Edition, World Scientific Publishing Co., Inc., Singapore, 1999.
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Garello, G., Morando, A. (2008). Regularity for Quasi-Elliptic Pseudo-Differential Operators with Symbols in Hölder Classes. In: Rodino, L., Wong, M.W. (eds) New Developments in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 189. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8969-7_11
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DOI: https://doi.org/10.1007/978-3-7643-8969-7_11
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