A Weak L Estimate for a Maximal Dyadic Sum Operator on R
نویسندگان
چکیده
Lacey and Thiele have recently obtained a new proof of Carleson’s theorem on almost everywhere convergence of Fourier series. This paper is a generalization of their techniques (known broadly as time-frequency analysis) to higher dimensions. In particular, a weaktype (2,2) estimate is derived for a maximal dyadic sum operator on Rn, n > 1. As an application one obtains a new proof of Sjölin’s theorem on weak L2 estimates for the maximal conjugated Calderón-Zygmund operator on Rn.
منابع مشابه
A Weak L 2 Estimate for a Maximal Dyadic
Lacey and Thiele have recently obtained a new proof of Carleson’s theorem on almost everywhere convergence of Fourier series. This paper is a generalization of their techniques (known broadly as time-frequency analysis) to higher dimensions. In particular, a weaktype (2,2) estimate is derived for a maximal dyadic sum operator on R, n > 1. As an application one obtains a new proof of Sjölin’s th...
متن کاملL Bounds for a Maximal Dyadic Sum Operator
The authors prove L bounds in the range 1 < p < ∞ for a maximal dyadic sum operator on R. This maximal operator provides a discrete multidimensional model of Carleson’s operator. Its boundedness is obtained by a simple twist of the proof of Carleson’s theorem given by Lacey and Thiele [6] adapted in higher dimensions [8]. In dimension one, the L boundedness of this maximal dyadic sum implies in...
متن کاملMaximal operator for pseudo-differential operators with homogeneous symbols
The aim of the present paper is to obtain a Sjölin-type maximal estimate for pseudo-differential operators with homogeneous symbols. The crux of the proof is to obtain a phase decomposition formula which does not involve the time traslation. The proof is somehow parallel to the paper by Pramanik and Terwilleger (P. Malabika and E. Terwilleger, A weak L2 estimate for a maximal dyadic sum operato...
متن کاملA Sharp Maximal Function Estimate for Vector-Valued Multilinear Singular Integral Operator
We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.
متن کاملThe sum of two maximal monotone operator is of type FPV
In this paper, we studied maximal monotonicity of type FPV for sum of two maximal monotone operators of type FPV and the obtained results improve and complete the corresponding results of this filed.
متن کامل