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Bilinear multipliers on Lorentz spaces

Francisco Villarroya (2008)

Czechoslovak Mathematical Journal

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves

Garth Gaudry, Tao Qian, Silei Wang (1996)

Colloquium Mathematicae

The aim of this paper is to study singular integrals T generated by holomorphic kernels defined on a natural neighbourhood of the set z ζ - 1 : z , ζ ∈ , z ≠ ζ , where is a star-shaped Lipschitz curve, = e x p ( i z ) : z = x + i A ( x ) , A ' ∈ L ∞ [ - π , π ] , A ( - π ) = A ( π ) . Under suitable conditions on F and z, the operators are given by (1) T F ( z ) = p . v . ∫ ( z η - 1 ) F ( η ) ( d η / η ) . We identify a class of kernels of the stated type that give rise to bounded operators on L 2 ( , | d | ) . We establish also transference results relating the boundedness of kernels on closed Lipschitz curves to corresponding results on periodic, unbounded curves.

Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.

Chun Li, Alan McIntosh, Tao Qian (1994)

Revista Matemática Iberoamericana

In the Fourier theory of functions of one variable, it is common to extend a function and its Fourier transform holomorphically to domains in the complex plane C, and to use the power of complex function theory. This depends on first extending the exponential function eixξ of the real variables x and ξ to a function eizζ which depends holomorphically on both the complex variables z and ζ .Our thesis is this. The natural analog in higher dimensions is to extend a function of m real variables monogenically...

Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

Jae Gil Choi, Sang Kil Shim (2023)

Czechoslovak Mathematical Journal

We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space ( H , B , ν ) . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space B . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur...

Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.

K. Trimèche (1996)

Collectanea Mathematica

In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.

Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates

María J. Carro, Elena Prestini (2009)

Studia Mathematica

We prove some extrapolation results for operators bounded on radial L p functions with p ∈ (p₀,p₁) and deduce some endpoint estimates. We apply our results to prove the almost everywhere convergence of the spherical partial Fourier integrals and to obtain estimates on maximal Bochner-Riesz type operators acting on radial functions in several weighted spaces.

Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications

Mejjaoli, H. (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35Q55,42B10.In this paper, we study the Schrödinger equation associated with the Dunkl operators, we study the dispersive phenomena and we prove the Strichartz estimates for this equation. Some applications are discussed.

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