Pseudodifferential operators and Hardy kernels on L p ( 𝐑 + )

Jeff E. Lewis; Cesare Parenti

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1980)

  • Volume: 7, Issue: 3, page 481-503
  • ISSN: 0391-173X

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Lewis, Jeff E., and Parenti, Cesare. "Pseudodifferential operators and Hardy kernels on $L^p(\mathbf {R}^+)$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.3 (1980): 481-503. <http://eudml.org/doc/83842>.

@article{Lewis1980,
author = {Lewis, Jeff E., Parenti, Cesare},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Hardy kernels; pseudodifferential operator; Hilbert transform; Mellin transform; symbol; parametrix; Laplace operator},
language = {eng},
number = {3},
pages = {481-503},
publisher = {Scuola normale superiore},
title = {Pseudodifferential operators and Hardy kernels on $L^p(\mathbf \{R\}^+)$},
url = {http://eudml.org/doc/83842},
volume = {7},
year = {1980},
}

TY - JOUR
AU - Lewis, Jeff E.
AU - Parenti, Cesare
TI - Pseudodifferential operators and Hardy kernels on $L^p(\mathbf {R}^+)$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1980
PB - Scuola normale superiore
VL - 7
IS - 3
SP - 481
EP - 503
LA - eng
KW - Hardy kernels; pseudodifferential operator; Hilbert transform; Mellin transform; symbol; parametrix; Laplace operator
UR - http://eudml.org/doc/83842
ER -

References

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  1. [A] A. Avantaggiati, Sistemi di equazioni a derivate parziali a coefficienti costanti in due variabili e problemi ellittici, Ricerche Mat., 24 (1975), pp. 203-279. Zbl0335.35042MR425330
  2. [CH] H.O. Cordes - E.A. Herman, Singular integral operators on a half-line, Proc. Nat. Acad. Sci. U.S.A., 56 (1966), pp. 1668-1673. Zbl0152.14201MR213918
  3. [E 1] G.I. Ěskin, Boundary value problems for elliptic pseudodifferential operators (in Russian), Nauka, Moscow (1973). 
  4. [E 2] G.I. Ěskin, General mixed boundary problems for elliptic differential equations, C.I.M.E., Course on Pseudodifferential Operators with Applications, II Ciclo (1977), Liguori, Napoli. Zbl0449.35021MR660650
  5. [FJL 1] E.B. Fabes - M. Jodeit, Jr. - J.E. Lewis, On the spectra of a Hardy kernel, J. Functional Analysis, 21 (1976), pp. 187-194. Zbl0321.47038MR394311
  6. [FJL 2] E.B. Fabes - M. Jodeit, Jr. - J.E. Lewis, Double layer potentials for domains with corners and edges, Indiana U. Math. J., 26 (1977), pp. 95-114. Zbl0363.35010MR432899
  7. [H] L. Hörmander, Translation invariant operators on Lp spaces, Acta Math., 104 (1960), pp. 93-139. Zbl0093.11402MR121655
  8. [N] J. Nourrigat, Une classe d'opérateurs pseudo-différentiels à une variable, C. R. Acad. Sci.Sér. A, tome283 (1976), pp. 457-460. Zbl0345.35091MR422920
  9. [P] B.A. Plamenevskii, An algebra of pseudodifferential operators in spaces with weight (in Russian), Mat. Sb., 106 (1978), pp. 297-320. Zbl0385.35055MR503596
  10. [Sh 1] E. Shamir, Reduced Hilbert transforms and singular integral equations, J. Analyse Math., 12 (1964), pp. 277-305. Zbl0173.14502MR165328
  11. [Sh 2] E. Shamir, Elliptic systems of singular integral operators. I: The half-space case, Trans. Amer. Math. Soc., 127 (1967), pp. 107-123. Zbl0157.19303MR215138
  12. [St] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. Zbl0207.13501MR290095

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