On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on $H^1$ and $BMO$

Chang, Der-Chen; Li, Song-Ying

On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on

H^{1}

and

B M O

Chang, Der-Chen; Li, Song-Ying

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 2, p. 341-356

MR 1736232 | Zbl 0952.42008

@article{ASNSP_1999_4_28_2_341_0,
     author = {Chang, Der-Chen and Li, Song-Ying},
     title = {On the boundedness of multipliers, commutators and the second derivatives of Green's operators on $H^1$ and $BMO$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {2},
     year = {1999},
     pages = {341-356},
     zbl = {0952.42008},
     mrnumber = {1736232},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_2_341_0}
}

Chang, Der-Chen; 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, Serie 4, Volume 28 (1999) no. 2, pp. 341-356. http://www.numdam.org/item/ASNSP_1999_4_28_2_341_0/

References

[C] D.C. Chang, The dual of Hardy spaces on a bounded domain in Rn, Forum Math. 6 (1994),65-81. | MR 1253178 | Zbl 0803.42014

[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. | MR 1458319 | Zbl 0917.35028

[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. | MR 1223705 | Zbl 0804.35027

[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. | MR 1191890 | Zbl 0772.35017

[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. | MR 1088476 | Zbl 0818.35023

[CW] R.R. Coifman - G. Weiss, "Analyse Harmonique Non-Commutative sur Certains Espaces Homogenes", Springer Lecture Notes 242, Springer-Verlag, Berlin, 1971. | MR 499948 | Zbl 0224.43006

[GT] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", 2nd Ed., Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983. | MR 737190 | Zbl 0562.35001

[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. | Zbl 0763.46024

[JK] D. Jerison - C.E. Kenig, Inhomogeneous Dirichlet problems in Lipschitz domains, J. Funct. Anal. 125 (1995). | MR 1331981 | Zbl 0832.35034

[KL] S.G. Krantz - S.Y. Li, Elliptic boundary value problems for the inhomogeneous Laplace equation on bounded domains, preprint.

[L] S.Y. Li, Toeplitz Operators on Hardy Space HP (S) with 0 < p ≤ 1, Integral Equations Operator Theory 15 (1992), 808-824. | Zbl 0781.47034

[NY] E. Nakai - K. Yabuta, Pointwise multipliersforfunctions of bounded mean oscilation, J. Math. Soc. Japan 37 (1985), 207-218. | MR 780660 | Zbl 0546.42019

[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. | MR 420326 | Zbl 0335.47018

[St] E.M. Stein, "Harmonic Analysis", Princeton University Press, Princeton, New Jersey, 1993. | MR 1232192 | Zbl 0821.42001

[T] G. Talenti, Sopra una classe di equazioni ellittiche a coefficienti misurabili, Ann. Mat. Pura Appl. (4) 69 (1965), 285-304. | MR 201816 | Zbl 0145.36602