Dashan Fan

Transference on certain multilinear multiplier operators

(Received 20 November 1999; revised 7 June 2000)Communicated by A. H. DooleyAbstractWe study DeLeeuw type theorem fors certai n multilinear operator ons th e Lebesgue spaces and on theHardy spaces A. s applications , on the toru s we obtain an analog of Lacey-Thieles theore onm thebilinear Hilbert transform, as well as analogie osf some recent theorems on multilinear singular integralsby Kenig-Stein and by Grafakos-Torres.2000 Mathematics subject classification: primary 42B15,42B20, 42B25.

^{} bounds for oscillatory hyper-Hilbert transform along curves

We study the oscillatory hyper-Hilbert transform (1) H n,α,β f(x) = ∫ 1 0 f(x-Γ(t))e ιt- t -1-α dt along the curve F(t) = (t p1 , t p2 , ···, t pn ), where p 1 , p 2 , ···, p n,α,β are some real positive numbers. We prove that if β > (n+ 1)α, then H n,α,β is bounded on L p whenever p ∈ (2β 2β-(n+1)α, (2β (n+1)α). Furthermore, we also prove that H n,α,β is bounded on L 2 when β = (n + 1)α. Our work improves and extends some known results by Chandarana in 1996 and in a preprint. As an application, we obtain an L p boundedness result for some strongly parabolic singular integrals with rough kernels.

DeLeeuw's theorem on Littlewood-Paley functions

We establish certain deLeeuw type theorems for Littlewood-Paley functions. By these theorems, we know that the boundedness of a Littlewood- Paley function on n is equivalent to the boundedness of its corresponding Littlewood-Paley function on the torus n . x1. Introduction Let R n be the n-dimensional Euclidean space and T n be the n-dimen- sional torus. T n can be identied with R n =, where is the unit lattice which is the additive group of points in R n having integral coordinates. For an L 1 (R n ) function we dene t(x) = 2 tn ( x=2 t ), t 2 R. Then the Fourier transform of t is ^ t( ) = ^ (2 t ). The Littlewood-Paley g-function

Regularity of some nonlinear quantities on superharmonic functions in local Herz-type Hardy spaces

In this paper, the authors introduce a kind of local Hardy spaces in

Regularity in Morrey Spaces of Strong Solutions to Nondivergence Elliptic Equations with VMO Coefficients

\Bbb R^n

WEAK TYPE (1,1) ESTIMATES FOR MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

associated with the local Herz spaces. Then the authors investigate the regularity in these local Hardy spaces of some nonlinear quantities on superharmonic functions on

A weighted norm inequality for rough singular integrals

\Bbb R^2

The method of rotation and Marcinkiewicz integrals on product domains

. The main results of the authors extend the corresponding results of Evans and Muller in a recent paper