A class of positive trigonometric sums. II.
A Class of Positive Trigonometrie Sums.
A class of tight framelet packets
This paper obtains a class of tight framelet packets on from the extension principles and constructs the relationships between the basic framelet packets and the associated filters.
A Cohen type inequality for Fourier expansions of orthogonal polynomials with a nondiscrete Jacobi-Sobolev inner product.
A Coifman-Rochberg type characterization of quasi-power weights.
A combinatorial derivation with Schröder paths of a determinant representation of Laurent biorthogonal polynomials.
A combinatorial representation with Schröder paths of biorthogonality of Laurent biorthogonal polynomials.
A commutator theorem for fractional integrals in spaces of homogeneous type.
A complete characterization of R-sets in the theory of differentiation of integrals
Let be the family of open rectangles in the plane ℝ² with a side of angle s to the x-axis. We say that a set S of directions is an R-set if there exists a function f ∈ L¹(ℝ²) such that the basis differentiates the integral of f if s ∉ S, and almost everywhere if s ∈ S. If the condition holds on a set of positive measure (instead of a.e.) we say that S is a WR-set. It is proved that S is an R-set (resp. a WR-set) if and only if it is a (resp. a ).
A condition for a two-weight norm inequality for singular integral operators
A convex polygon as a discrete plane curve.
A convolution inequality concerning Cantor-Lebesgue measures.
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 counterexample for the strong maximal operator
A counterexample in harmonic analysis
A counter-example in singular integral theory
An improvement of a lemma of Calderón and Zygmund involving singular spherical harmonic kernels is obtained and a counter-example is given to show that this result is best possible. In a particular case when the singularity is O(|log r|), let and suppose f vanishes outside of a compact subset of , N ≥ 2. Also, let k(x) be a Calderón-Zygmund kernel of spherical harmonic type. Suppose f(x) = O(|log r|) as r → 0 in the -sense. Set . Then F(x) = O(log²r) as r → 0 in the -sense, 1 < p < ∞....
A Counterexample on Nontangential Convergence for Oscillatory Integrals
A counterexample to an assertion due to Blumenthal.