Multiparameter singular integrals and maximal operators along flat surfaces | Zendy

Yong-Kum Cho | Zendy; Sunggeum Hong | Zendy; Joonil Kim | Zendy; Chan Woo Yang | Zendy

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Multiparameter singular integrals and maximal operators along flat surfaces

Author(s) -

Yong-Kum Cho,

Sunggeum Hong,

Joonil Kim,

Chan Woo Yang

Publication year - 2008

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/566

Subject(s) - mathematics , singular integral , singular integral operators , geometry , mathematical analysis , integral equation

We study double Hilbert transforms and maximal functions along surfaces of the form (t1, t2, γ1(t1)γ2(t2)). The Lp(R3) boundedness of the maximal operator is obtained if each γi is a convex increasing and γi(0) = 0. The double Hilbert transform is bounded in Lp(R3) if both γi’s above are extended as even functions. If γ1 is odd, then we need an additional comparability condition on γ2. This result is extended to higher dimensions and the general hyper-surfaces of the form (t1, . . . , tn,Γ(t1, . . . , tn)) on Rn+1.

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