A correction to the paper "A multiplier theorem for Jacobi expansion" Studia Math. 52 (1975), pp. 234-261
A general theorem on Nörlund summability of Fourier series with applications
A Littlewood-Paley inequality for arbitrary intervals.
A Littlewood-Paley Inequality for the Carleson Operator.
A multiplier theorem for Jacobi expansions
A new criterion for the absolute Riesz summability of the conjugate series of a Fourier series
A note on a conjecture of D. Oberlin
A note on the Littlewood-Paley square function inequality
A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
A sharp correction theorem
Under certain conditions on a function space X, it is proved that for every -function f with one can find a function φ, 0 ≤ φ ≤ 1, such that φf ∈ X, and . For X one can take, e.g., the space of functions with uniformly bounded Fourier sums, or the space of -functions on whose convolutions with a fixed finite collection of Calderón-Zygmund kernels are also bounded.
A strengthening of a theorem of Marcinkiewicz
We consider a problem of intervals raised by I. Ya. Novikov in [Israel Math. Conf. Proc. 5 (1992), 290], which refines the well-known theorem of J. Marcinkiewicz concerning structure of closed sets [A. Zygmund, Trigonometric Series, Vol. I, Ch. IV, Theorem 2.1]. A positive solution to the problem for some specific cases is obtained. As a result, we strengthen the theorem of Marcinkiewicz for generalized Cantor sets.
A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform
Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space . We show that if W and its inverse both satisfy a matrix reverse Hölder property introduced by Christ and Goldberg, then the weighted Hilbert transform and also all weighted dyadic martingale transforms are bounded. We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform.
A uniform estimate for quartile operators.
There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove Lp estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model...
Allied integrals, functions, and series for the unit sphere.
An estimate of the rate convergence of Cesaro means of Fourier Stieltjes series and its conjugate series
Boundary value problems for analytic and harmonic functions in domains with nonsmooth boundaries. Applications to conformal mappings.
Bounds for oscillatory integrals and L²-theory of the corresponding singular integrals
Characterisations of H... by singular intetgral transforms on martingales and R...
Commutators with fractional integral operators
We investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for and α/n + 1/q = 1/p, the norm is equivalent to the norm of b in the weighted BMO space BMO(ν), where . This work extends some of the results on this topic existing in the literature, and continues a line of investigation which was initiated by Bloom in 1985 and was recently developed further by the first author, Lacey, and Wick.
Continuous generalized Toeplitz kernels in R