A distributional convolution for a generalized finite Fourier transformation

In this paper we define a generalized finite Fourier transformation in distribution spaces. Also we investigate a distributional convolution for this finite integral transformation.

     

Variable exponent Hardy spaces associated with discrete Laplacians on graphs

In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.     

Calderón–Zygmund operators in the Bessel setting

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood–Paley–Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calderón–Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.     

On Hardy spaces associated with Bessel operators

In this paper, we study Hardy spaces associated with two Bessel operators. Two different kind of Hardy spaces appear. These differences are transparent in the corresponding atomic decompositions. The first author was partially supported by MTM2004/05878. The second author was supported by the European Commission Marie Curie Host Fellowship for the Transfer of Knowledge “Harmonic Analysis, Nonlinear Analysis and Probability” MTKD-CT-2004-013389 and by Polish funds for science in years 2005–2008 (research project 1P03A03029).     

Paley-wiener theorems for the Hankel transformation

In this paper we establish new Paley-Wiener type theorems for the Hankel transformation.     

Transferring Boundedness from Conjugate Operators Associated with Jacobi, Laguerre, and Fourier–Bessel Expansions to Conjugate Operators in the Hankel Setting

In this paper we establish transference results showing that the boundedness of the conjugate operator associated with Hankel transforms on Lorentz spaces can be deduced from the corresponding boundedness of the conjugate operators defined on Laguerre, Jacobi, and Fourier–Bessel settings. Our result also allows us to characterize the power weights in order that conjugation associated with Laguerre, Jacobi, and Fourier–Bessel expansions define bounded operators between the corresponding weighted L ^p spaces. This paper is partially supported by MTM2004/05878. Third and fourth authors are also partially supported by grant PI042004/067.     

Trevoagenins C and D,dammarane triterpenes from Trevoa trinervis miers.

Trevoagenins C and D are minor triterpenes isolated from Trevoa trinervis Miers. The structure of trevoagenin C was established by chemical and spectroscopic means that of trevoagenin D by X-ray diffraction techniques.     

Spaces of type and the Hankel convolution

In this paper we introduce new function spaces that are denoted by , -1/2$"> and and that are spaces of type where the Hankel convolution and the Hankel transformation are defined. The spaces will play the same role in the Hankel setting that the spaces play in the theory of Fourier transformation.