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Singular integrals with highly oscillating kernels on product spaces

Elena Prestini (2000)

Colloquium Mathematicae

We prove the L 2 ( 2 ) boundedness of the oscillatory singular integrals P 0 f ( x , y ) = ∫ D x e i ( M 2 ( x ) y ' + M 1 ( x ) x ' ) ο v e r x ' y ' f ( x - x ' , y - y ' ) d x ' d y ' for arbitrary real-valued L ∞ functions M 1 ( x ) , M 2 ( x ) and for rather general domains D x ⊆ 2 whose dependence upon x satisfies no regularity assumptions.

Solving dual integral equations on Lebesgue spaces

Óscar Ciaurri, José Guadalupe, Mario Pérez, Juan Varona (2000)

Studia Mathematica

We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh’s type. We reformulate these equations giving a better description in terms of continuous operators on L p spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series ∑ n = 0 ∞ c n J μ + 2 n + 1 which converges in the L p -norm and almost everywhere, where J ν denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution....

Some class of polynomial hypergroups

Wojciech Młotkowski (2006)

Banach Center Publications

We provide explicit formulas for linearizing coefficients for some class of orthogonal polynomials.

Some classical function systems in separable Orlicz spaces

C. Finet, G. Tkebuchava (1996)

Studia Mathematica

The boundedness of (sub)sequences of partial Fourier and Fourier-Walsh sums in subspaces of separable Orlicz spaces is studied. The boundedness of the shift operator and Paley function with respect to the Haar system is also investigated. These results are applied to get the analogues of the classical theorems on basicness of the trigonometric and Walsh systems in nonreflexive separable Orlicz spaces.

Some Coefficient Estimates for Polynomials on the Unit Interval

Qazi, M. A., Rahman, Q. I. (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.In this paper we present some inequalities about the moduli of the coefficients of polynomials of the form f (x) : = еn = 0nan xn, where a0, ј, an О C. They can be seen as generalizations, refinements or analogues of the famous inequality of P. L. Chebyshev, according to which |an| Ј 2n-1 if | еn = 0n an xn | Ј 1 for -1 Ј x Ј 1.

Some eigenvalue estimates for wavelet related Toeplitz operators

Krzysztof Nowak (1993)

Colloquium Mathematicae

By a straightforward computation we obtain eigenvalue estimates for Toeplitz operators related to the two standard reproducing formulas of the wavelet theory. Our result extends the estimates for Calderón-Toeplitz operators obtained by Rochberg in [R2]. In the first section we recall two standard reproducing formulas of the wavelet theory, we define Toeplitz operators and discuss some of their properties. The second section contains precise statements of our results and their proofs. At the end...

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