L p and Hölder estimates for pseudodifferential operators : sufficient conditions

Richard Beals

Annales de l'institut Fourier (1979)

  • Volume: 29, Issue: 3, page 239-260
  • ISSN: 0373-0956

Abstract

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Continuity in L p spaces and spaces of Hölder type is proved for pseudodifferential operators of order zero, under general conditions on the class of symbols. Applications to the regularity theory of some hypoelliptic operators are outlined.

How to cite

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Beals, Richard. "$L^p$ and Hölder estimates for pseudodifferential operators : sufficient conditions." Annales de l'institut Fourier 29.3 (1979): 239-260. <http://eudml.org/doc/74422>.

@article{Beals1979,
abstract = {Continuity in $L^p$ spaces and spaces of Hölder type is proved for pseudodifferential operators of order zero, under general conditions on the class of symbols. Applications to the regularity theory of some hypoelliptic operators are outlined.},
author = {Beals, Richard},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {239-260},
publisher = {Association des Annales de l'Institut Fourier},
title = {$L^p$ and Hölder estimates for pseudodifferential operators : sufficient conditions},
url = {http://eudml.org/doc/74422},
volume = {29},
year = {1979},
}

TY - JOUR
AU - Beals, Richard
TI - $L^p$ and Hölder estimates for pseudodifferential operators : sufficient conditions
JO - Annales de l'institut Fourier
PY - 1979
PB - Association des Annales de l'Institut Fourier
VL - 29
IS - 3
SP - 239
EP - 260
AB - Continuity in $L^p$ spaces and spaces of Hölder type is proved for pseudodifferential operators of order zero, under general conditions on the class of symbols. Applications to the regularity theory of some hypoelliptic operators are outlined.
LA - eng
UR - http://eudml.org/doc/74422
ER -

References

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  1. [1] R. BEALS, Lp and Hölder estimates for pseudodifferential operators : necessary conditions, Amer. Math. Soc. Proc. Symp. Pure Math., to appear. Zbl0418.35085
  2. [2] A.P. CALDERON, Lebesgue space of differentiable functions and distributions, Amer. Math. Soc. Proc. Symp. Pure Math., 5 (1961), 33-49. Zbl0195.41103MR26 #603
  3. [3] C.-H. CHING, Pseudo-differential operators with non-regular symbols, J. Differential Equations, 11 (1972), 436-447. Zbl0248.35106MR45 #5823
  4. [4] R.R. COIFMAN and G. WEISS, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, no. 242, Springer-Verlag, Berlin, 1971. Zbl0224.43006MR58 #17690
  5. [5] L. HORMANDER, The Weyl calculus of pseudodifferential operators, to appear. Zbl0388.47032
  6. [6] Y. KANNAI, An unsolvable hypoelliptic differential operator, Israel J. Math., 9 (1971), 306-315. Zbl0211.40601MR43 #2573
  7. [7] H. KUMANO-GO and K. TANIGUCHI, Oscillatory integrals of symbols of operators on Rn and operators of Fredholm type, Proc. Japan Acad., 49 (1973), 397-402. Zbl0272.47032MR50 #8167
  8. [8] K. MILLER, Parametrices for a class of hypoelliptic operators, J. Differential Equations, to appear. Zbl0409.35022
  9. [9] A. NAGEL and E.M. STEIN, A new class of pseudo-differential operators, Proc. Nat. Acad. Sci. U.S.A., 75 (1978), 582-585. Zbl0376.35053MR58 #7222
  10. [10] A. UNTERBERGER, Symboles associés aux champs de repères de la forme symplectique, C.R. Acad. Sci., Paris, sér. A, 245 (1977), 1005-1008. Zbl0381.47025MR58 #24411

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