Gel\cprime fer functions, integral means, bounded mean oscillation, and univalency

Mean oscillation of functions

The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantiied way using various function spaces. In particular, the results in this paper show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. Several open questions about spaces of sequences are answere...

Multilinear integral operators and mean oscillation

Let b ∈ BMO(Rn) and T be the Calderón–Zygmund singular integral operator. The commutator [b,T ] generated by b and T is defined by [b,T ] f (x) = b(x)T f (x)−T (b f )(x). By a classical result of Coifman et al [6], we know that the commutator is bounded on Lp(Rn) for 1 < p < ∞. Chanillo [1] proves a similar result when T is replaced by the fractional integral operators. In [9], the boundedness ...

Vector Valued Measures of Bounded Mean Oscillation

The duality between Hl and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained . Using the atomic decomposition approach ([C], [L]) the author studied the problem of characterizing the dual space of Hl of vector-valued functions . In [B2] the author showed, for the case SZ = {Iz1 = 1}, tha...

Integral Means of Multivalent Functions

For analytic functions f(z) and g(z) which satisfy the subordination f(z) ≺ g(z), J. E. Littlewood (Proc. London Math. Soc., 23 (1925), 481–519) has shown some interesting results for integral means of f(z) and g(z). The object of the present paper is to derive some applications of integral means by J.E. Littlewood and show interesting examples for our theorems. We also generalize the results o...

Estimates of Multilinear Singular Integral Operators and Mean Oscillation