Compensated Compactness, Separately Convex Functions and Interpolatory Estimates between Riesz Transforms and Haar Projections

Compensated Compactness, Separately convex Functions and Interpolatory Estimates between Riesz Transforms and Haar Projections

5 The Proof of Theorem 2.1. 27 5.1 Estimates for Tl,m, l ≥ 0, m < −l. . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.2 Estimates for Tl,m, l ≥ 0, m > 0. . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.3 Estimates for Tl,m, l ≥ 0, −l ≤ m ≤ 0. . . . . . . . . . . . . . . . . . . . . . . . 33 5.4 Estimates for T (ε) l R −1 i0 , l ≥ 0. . . . . . . . . . . . . . . . . . . . . . . . ...

The Norm Estimates of Pre-Schwarzian Derivatives of Spirallike Functions and Uniformly Convex $alpha$-spirallike Functions

For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$,  we definea  subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In  the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative  $mathrm{T}...

Isometric Immersions and Compensated Compactness

A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold M2 which can be realized as isometric immersions into R3. This problem can be formulated as initial and/or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic-hyperbolic type whose mathematical theory is largely incomplete. I...

Dimension free estimates for the oscillation of Riesz transforms

In this paper we establish dimension free Lp(Rn, |x|α) norm inequalities (1 < p < ∞) for the oscillation and variation of the Riesz transforms in Rn. In doing so we find Ap−weighted norm inequalities for the oscillation and the variation of the Hilbert transform in R. Some weighted transference results are also proved. INTRODUCTION Throughout (X,F , μ) will denote an arbitrary σ−finite measure ...

On compactness and projections