A characterization of localized Bessel potential spaces and applications to Jacobi and Henkel multipliers
A convolution property of the Cantor-Lebesgue measure
A convolution property of the Cantor-Lebesgue measure, II
For 1 ≤ p,q ≤ ∞, we prove that the convolution operator generated by the Cantor-Lebesgue measure on the circle is a contraction whenever it is bounded from to . We also give a condition on p which is necessary if this operator maps into L²().
A correction to the paper "A multiplier theorem for Jacobi expansion" Studia Math. 52 (1975), pp. 234-261
A Littlewood-Paley inequality for arbitrary intervals.
A multiplier characterization of analytic UMD spaces
A multiplier theorem for Jacobi expansions
A multiplier theorem for ultraspherical series
A new classification of periodic functions and their approximation
A relation between Fourier transforms in one and two variables
A Universal Topology for Sequence Spaces.
A variation norm Carleson theorem
We strengthen the Carleson-Hunt theorem by proving estimates for the -variation of the partial sum operators for Fourier series and integrals, for . Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.
Absolute convergence of multiple Fourier integrals
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of integrability of the function and its partial derivatives, each with a different p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.
Absolute Nörlund summability factors of power series and Fourier series
Four theorems of Ahmad [1] on absolute Nörlund summability factors of power series and Fourier series are proved under weaker conditions.
Almost everywhere convergence of Fourier integrals in Rn
Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an L2-localisation principle.
An Hp Inequality for Strongly Singular Integrals.
An -theory of the generalized Stokes resolvent system in infinite cylinders
Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with , a bounded domain of class , are obtained in the space , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.
An -functional calculus for power-bounded operators on certain UMD spaces
For 1 ≤ q < ∞, let denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction q >...
An uniform boundedness for Bochner-Riesz operators related to the Hankel transform.