On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on H 1 and B M O

Der-Chen Chang; Song-Ying Li

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1999)

  • Volume: 28, Issue: 2, page 341-356
  • ISSN: 0391-173X

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Chang, Der-Chen, and Li, Song-Ying. "On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on $H^1$ and $BMO$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 28.2 (1999): 341-356. <http://eudml.org/doc/84380>.

@article{Chang1999,
author = {Chang, Der-Chen, Li, Song-Ying},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {multipliers; commutators; Green operator; Dirichlet problem; elliptic equation; Hardy space; ; BMO; Calderón-Zygmund singular integral operators},
language = {eng},
number = {2},
pages = {341-356},
publisher = {Scuola normale superiore},
title = {On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on $H^1$ and $BMO$},
url = {http://eudml.org/doc/84380},
volume = {28},
year = {1999},
}

TY - JOUR
AU - Chang, Der-Chen
AU - Li, Song-Ying
TI - On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on $H^1$ and $BMO$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1999
PB - Scuola normale superiore
VL - 28
IS - 2
SP - 341
EP - 356
LA - eng
KW - multipliers; commutators; Green operator; Dirichlet problem; elliptic equation; Hardy space; ; BMO; Calderón-Zygmund singular integral operators
UR - http://eudml.org/doc/84380
ER -

References

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  1. [C] D.C. Chang, The dual of Hardy spaces on a bounded domain in Rn, Forum Math. 6 (1994),65-81. Zbl0803.42014MR1253178
  2. [CDS] D.C. Chang - G. Dafni - E.M. Stein, Hardy spaces, BMO, and elliptic boundary value problems on a smooth domain in Rn, Trans. Amer. Math. Soc.351 (1999), 1605-1666. Zbl0917.35028MR1458319
  3. [CKS] D.C. Chang - S.G. Krantz - E.M. Stein, HP theory on a smooth domain in R N and elliptic boundary value problems, J. Funct. Anal.114 (1993), 286-347. Zbl0804.35027MR1223705
  4. [CFL1] F. Chiarenza - M. Frasca - P. Longo, Interior W2,p estimates for non divergence elliptic equations with discontinuous coefficients, Ricerche Mat.40 (1991), 149-168. Zbl0772.35017MR1191890
  5. [CFL2] F. Chiarenza - M. Frasca - P. Longo, W2,p-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients, Trans. Amer. Math. Soc.336 (1993), 841-853. Zbl0818.35023MR1088476
  6. [CW] R.R. Coifman - G. Weiss, "Analyse Harmonique Non-Commutative sur Certains Espaces Homogenes", Springer Lecture Notes242, Springer-Verlag, Berlin, 1971. Zbl0224.43006MR499948
  7. [GT] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", 2nd Ed., Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983. Zbl0562.35001MR737190
  8. [HJMT] Y.S. Han - B. Jawerth - M. Taibleson - G. Weiss, Littlewood-Paley theory and ε-families of operators, Colloq. Math.LX/LXI (1990), 321-359. Zbl0763.46024
  9. [JK] D. Jerison - C.E. Kenig, Inhomogeneous Dirichlet problems in Lipschitz domains, J. Funct. Anal.125 (1995). Zbl0832.35034MR1331981
  10. [KL] S.G. Krantz - S.Y. Li, Elliptic boundary value problems for the inhomogeneous Laplace equation on bounded domains, preprint. 
  11. [L] S.Y. Li, Toeplitz Operators on Hardy Space HP (S) with 0 &lt; p ≤ 1, Integral Equations Operator Theory15 (1992), 808-824. Zbl0781.47034
  12. [NY] E. Nakai - K. Yabuta, Pointwise multipliersforfunctions of bounded mean oscilation, J. Math. Soc. Japan37 (1985), 207-218. Zbl0546.42019MR780660
  13. [S] D.A. Stegenga, Bounded Toeplitz operators on H1 and applications of duality between H1 and functions of bounded mean oscillation, Amer. J. Math. (1976), 573-589. Zbl0335.47018MR420326
  14. [St] E.M. Stein, "Harmonic Analysis", Princeton University Press, Princeton, New Jersey, 1993. Zbl0821.42001MR1232192
  15. [T] G. Talenti, Sopra una classe di equazioni ellittiche a coefficienti misurabili, Ann. Mat. Pura Appl. (4) 69 (1965), 285-304. Zbl0145.36602MR201816

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