Boundedness of the Hausdorff operators in spaces, 0 < p < 1
Sufficient conditions for the boundedness of the Hausdorff operators in the Hardy spaces , 0 < p < 1, on the real line are proved. Two related negative results are also given.
C1 Changes of Variable: Beurling-Helson Type Theorem and Hörmander Conjecture on Fourier Multipliers.
Calderón's Formula Associated with a Differential Operator on (0, ...) and Inversion of the Generalized Abel Transform.
Carleson's Theorem: proof, complements, variations.
Carleson's Theorem from 1965 states that the partial Fourier sums of a square integrable function converge pointwise. We prove an equivalent statement on the real line, following the method developed by the author and C. Thiele. This theorem, and the proof presented, is at the center of an emerging theory which complements the statement and proof of Carleson's theorem. An outline of these variations is also given.
Causality and local analyticity : mathematical study
Characterization of measures in the group C*-algebra of a locally compact group.
Complex powers and asymptotic expansions. I. Functions of certain types.
Complex powers and asymptotic expansions. II.
Continuous linear right inverses for convolution operators in spaces of real analytic functions
We determine the convolution operators on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).
Corrections to the Papers "Power Bounded Matrices of Fourier-Stieltjes Transforms I, II".
Counterexamples for classical operators on Lorentz-Zygmund spaces
Critical length for a Beurling type theorem
In a recent paper [3] C. Baiocchi, V. Komornik and P. Loreti obtained a generalisation of Parseval's identity by means of divided differences. We give here a proof of the optimality of that theorem.
Damping oscillatory integrals with polynomial phase.
Die Theorie der Fourier'schen Integrale und Formeln
Double Fourier Series with Coefficients O (n m) -1.
Ein Äquikonvergenzsatz für eine Klasse von singulären Differentialoperatoren.
Eine Erweiterung des Riemann-Lebesgue-Lemmas.
Entrelacement de co-Poisson
On connaît le lien intime qui existe entre les équations fonctionnelles des fonctions et les formules sommatoires dont le prototype est donné par celle de Poisson. Ce lien fait intervenir la transformation intégrale de Fourier et ses généralisations. Ici, nous réexaminons la signification harmonique (ainsi qu’hilbertienne et distributionnelle) des équations fonctionnelles ayant la forme la plus simple, à savoir, celle s’appliquant pour la fonction dzêta de Riemann et les séries de Dirichlet...
Estimates of one-dimensional oscillatory integrals
We study one-dimensional oscillator integrals which arise as Fourier-Stieltjes transforms of smooth, compactly supported measures on smooth curves in Euclidean spaces and determine their decay at infinity, provided the curves satisfy certain geometric conditions.
Extension of a Theorem of Fejér to Double Fourier-Stieltjes Series.