Bilinear Calderón-Zygmund operator and its commutator on some variable exponent spaces of homogeneous type

Guanghui Lu

Article Details

Bilinear Calderón-Zygmund operator and its commutator on some variable exponent spaces of homogeneous type

Authors:

Guanghui Lu

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 2, pp.433-456

Document Type:

Article

Publication Date:

4/2024

Document Language:

English

Document ID (Org No.):

2001315589

pISSN:

2651-477X

Keywords:

Abstract:

 Let X,d,mu be a space of homogeneous type in the sense of Coifman and and Weiss. In this setting, the author proves that a bilinear Calderon-Zygmund operator is bounded from the product of variable exponent Lebesgue spaces Lp_1cdotXtimes Lp_2cdotX into spaces LpcdotX, and it is bounded from the product of variable exponent generalized Morrey spaces mathcalLp_1cdot,varphi_1Xtimes mathcalLp_2cdot,varphi_2X into spaces mathcalLpcdot,varphiX, where the Lebesgue measure functions varphicdot,cdot, varphi_1cdot,cdot and varphi_2cdot,cdot satisfy varphi_1timesvarphi_2varphi, and frac1pcdotfrac1p_1cdotfrac1p_2cdot. Furthermore, by establishing sharp maximal estimate for the commutator b_1,b_2,BT generated by b_1, b_2inmathrmBMOX and BT, the author shows that the b_1,b_2,BT is bounded from the product of spaces Lp_1cdotXtimes Lp_2cdotX into spaces LpcdotX, and it is also bounded from product of spaces mathcalLp_1cdot,varphi_1Xtimes mathcalLp_2cdot,varphi_2X into spaces Lpcdot,varphiX.

 Let X,d,mu be a space of homogeneous type in the sense of Coifman and and Weiss. In this setting, the author proves that a bilinear Calderon-Zygmund operator is bounded from the product of variable exponent Lebesgue spaces Lp_1cdotXtimes Lp_2cdotX into spaces LpcdotX, and it is bounded from the product of variable exponent generalized Morrey spaces mathcalLp_1cdot,varphi_1Xtimes mathcalLp_2cdot,varphi_2X into spaces mathcalLpcdot,varphiX, where the Lebesgue measure functions varphicdot,cdot, varphi_1cdot,cdot and varphi_2cdot,cdot satisfy varphi_1timesvarphi_2varphi, and frac1pcdotfrac1p_1cdotfrac1p_2cdot. Furthermore, by establishing sharp maximal estimate for the commutator b_1,b_2,BT generated by b_1, b_2inmathrmBMOX and BT, the author shows that the b_1,b_2,BT is bounded from the product of spaces Lp_1cdotXtimes Lp_2cdotX into spaces LpcdotX, and it is also bounded from product of spaces mathcalLp_1cdot,varphi_1Xtimes mathcalLp_2cdot,varphi_2X into spaces Lpcdot,varphiX.

 Let X,d,mu be a space of homogeneous type in the sense of Coifman and and Weiss. In this setting, the author proves that a bilinear Calderon-Zygmund operator is bounded from the product of variable exponent Lebesgue spaces Lp_1cdotXtimes Lp_2cdotX into spaces LpcdotX, and it is bounded from the product of variable exponent generalized Morrey spaces mathcalLp_1cdot,varphi_1Xtimes mathcalLp_2cdot,varphi_2X into spaces mathcalLpcdot,varphiX, where the Lebesgue measure functions varphicdot,cdot, varphi_1cdot,cdot and varphi_2cdot,cdot satisfy varphi_1timesvarphi_2varphi, and frac1pcdotfrac1p_1cdotfrac1p_2cdot. Furthermore, by establishing sharp maximal estimate for the commutator b_1,b_2,BT generated by b_1, b_2inmathrmBMOX and BT, the author shows that the b_1,b_2,BT is bounded from the product of spaces Lp_1cdotXtimes Lp_2cdotX into spaces LpcdotX, and it is also bounded from product of spaces mathcalLp_1cdot,varphi_1Xtimes mathcalLp_2cdot,varphi_2X into spaces Lpcdot,varphiX.

 Let X,d,mu be a space of homogeneous type in the sense of Coifman and and Weiss. In this setting, the author proves that a bilinear Calderon-Zygmund operator is bounded from the product of variable exponent Lebesgue spaces Lp_1cdotXtimes Lp_2cdotX into spaces LpcdotX, and it is bounded from the product of variable exponent generalized Morrey spaces mathcalLp_1cdot,varphi_1Xtimes mathcalLp_2cdot,varphi_2X into spaces mathcalLpcdot,varphiX, where the Lebesgue measure functions varphicdot,cdot, varphi_1cdot,cdot and varphi_2cdot,cdot satisfy varphi_1timesvarphi_2varphi, and frac1pcdotfrac1p_1cdotfrac1p_2cdot. Furthermore, by establishing sharp maximal estimate for the commutator b_1,b_2,BT generated by b_1, b_2inmathrmBMOX and BT, the author shows that the b_1,b_2,BT is bounded from the product of spaces Lp_1cdotXtimes Lp_2cdotX into spaces LpcdotX, and it is also bounded from product of spaces mathcalLp_1cdot,varphi_1Xtimes mathcalLp_2cdot,varphi_2X into spaces Lpcdot,varphiX.

Article Details

Bilinear Calderón-Zygmund operator and its commutator on some variable exponent spaces of homogeneous type

Authors:

Guanghui Lu

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 2, pp.433-456

Document Type:

Article

Publication Date:

4/2024

Document Language:

English

Document ID (Org No.):

2001315589

pISSN:

2651-477X

space of homogeneous type

bilinear Calderón-Zygmund operator

commutator

space BMO(X)

variable exponent generalized Morrey space

Issues

Article Details

Bilinear Calderón-Zygmund operator and its commutator on some variable exponent spaces of homogeneous type

Authors: Guanghui Lu

Publisher: Hacettepe University

Main Topics: Mathematical Sciences

Journal: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 2, pp.433-456

Document Type: Article

Publication Date: 4/2024

Document Language: English

Document ID (Org No.): 2001315589

pISSN: 2651-477X

space of homogeneous type

bilinear Calderón-Zygmund operator

commutator

space BMO(X)

variable exponent generalized Morrey space

Issues

Authors:

Guanghui Lu

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 2, pp.433-456

Document Type:

Article

Publication Date:

4/2024

Document Language:

English

Document ID (Org No.):

2001315589

pISSN:

2651-477X