Triangulations of closed sets and bases in function spaces.
Triebel-Lizorkin spaces for Hermite expansions
This paper develops some Littlewood-Paley theory for Hermite expansions. The main result is that certain analogues of Triebel-Lizorkin spaces are well-defined in the context of Hermite expansions.
Triebel-Lizorkin spaces on spaces of homogeneous type
In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where , and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].
Triebel-Lizorkin spaces with non-doubling measures
Suppose that μ is a Radon measure on , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality...
Trigonometric approximation by Nörlund type means in -norm
We show that the same degree of approximation as in the theorems proved by L. Leindler [Trigonometric approximation in -norm, J. Math. Anal. Appl. 302 (2005), 129–136] and P. Chandra [Trigonometric approximation of functions in -norm, J. Math. Anal. Appl. 275 (2002), 13–26] is valid for a more general class of lower triangular matrices. We also prove that these theorems are true under weakened assumptions.
Trigonometric approximation in the norms and seminorm
Trigonometric interpolation for bivariate functions of bounded variation
Trigonometric interpolation, III
Trigonometric interpolation, IV
Trigonometric interpolation, V
Trigonometric Polynomial Approximation in the L1-Form.
Trigonometric series with gaps
Trigonometric series with -monotone coefficients in spaces with mixed quasinorm.
Trigonometrie Approximation with Exponential Error Orders. I. Construction of Asymptotically Optimal Processes; Generalized de la Vallée Poussin Sums.
Trigonometrische Reihen über multiplikativen Zahlenmengen.
Triple Hilbert transforms along polynomial surfaces in .
Twisted convolutions with Calderón-Zygmund kernels.
Two complete and minimal systems associated with the zeros of the Riemann zeta function
We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the “dual Poisson formula” of Duffin-Weinberger (also named by us co-Poisson formula), and the “Sonine spaces” of entire functions defined and studied by de Branges. We determine in which (extended) Sonine spaces the zeros define a complete, or minimal, system. We obtain some general results dealing with the distribution of the zeros of the de-Branges-Sonine entire functions. We...
Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series
We establish two new norm convergence theorems for Henstock-Kurzweil integrals. In particular, we provide a unified approach for extending several results of R. P. Boas and P. Heywood from one-dimensional to multidimensional trigonometric series.
Two endpoint bounds for generalized Radon transforms in the plane.