TY - JOUR

T1 - Boundedness of singular integral operators with variable kernels

AU - Lee, Ming Yi

AU - Lin, Chin Cheng

AU - Lin, Ying Chieh

AU - Yan, Dunyan

N1 - Funding Information:
E-mail addresses: [email protected] (M.-Y. Lee), [email protected] (C.-C. Lin), [email protected] (Y.-C. Lin), [email protected] (D. Yan). 1 Research supported by NSC of Taiwan under Grant #NSC 96-2628-M-008-017. 2 Research supported by NSC of Taiwan under Grant #NSC 96-2115-M-008-002. 3 Research supported by NSF of China under Grants 10571014 and 10631080.

PY - 2008/12/15

Y1 - 2008/12/15

N2 - Let K be a generalized Calderón-Zygmund kernel defined on Rn × (Rn {set minus} {0}). The singular integral operator with variable kernel given byT f (x) = p.v. under(∫, Rn) K (x, x - y) f (y) d y is studied. We show that if the kernel K (x, y) satisfies the Lq-Hörmander condition with respect to x and y variables, respectively, then T is bounded on Lwp. If we add an extra Dini type condition on K, then we may show the Hwp - Lwp boundedness of T.

AB - Let K be a generalized Calderón-Zygmund kernel defined on Rn × (Rn {set minus} {0}). The singular integral operator with variable kernel given byT f (x) = p.v. under(∫, Rn) K (x, x - y) f (y) d y is studied. We show that if the kernel K (x, y) satisfies the Lq-Hörmander condition with respect to x and y variables, respectively, then T is bounded on Lwp. If we add an extra Dini type condition on K, then we may show the Hwp - Lwp boundedness of T.

KW - A weights

KW - L-Dini condition

KW - L-Hörmander condition

KW - Singular integral operators

KW - Variable kernel

UR - http://www.scopus.com/inward/record.url?scp=51249083444&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2008.07.078

DO - 10.1016/j.jmaa.2008.07.078

M3 - 期刊論文

AN - SCOPUS:51249083444

SN - 0022-247X

VL - 348

SP - 787

EP - 796

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -