Displaying similar documents to “A Fourier inequality with Ap and weak-L1 weight.”

The class Bpfor weighted generalized Fourier transform inequalities

Chokri Abdelkefi, Mongi Rachdi (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In the present paper, we prove weighted inequalities for the Dunkl transform (which generalizes the Fourier transform) when the weights belong to the well-known class Bp. As application, we obtain the Pitt’s inequality for power weights.

Weighted L boundedness of Fourier series with respect to generalized Jacobi weights.

José J. Guadalupe, Mario Pérez, Francisco J. Ruiz, Juan L. Varona (1991)

Publicacions Matemàtiques

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Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Sf denote the n-th partial sum of the Fourier series of f in the orthogonal polynomials associated to w. We prove a result about uniform boundedness of the operators S in some weighted L spaces. The study of the norms of the kernels K related to the operators S allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.

First and second order Opial inequalities

Steven Bloom (1997)

Studia Mathematica

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Let T γ f ( x ) = ʃ 0 x k ( x , y ) γ f ( y ) d y , where k is a nonnegative kernel increasing in x, decreasing in y, and satisfying a triangle inequality. An nth-order Opial inequality has the form ʃ 0 ( i = 1 n | T γ i f ( x ) | q i | ) | f ( x ) | q 0 w ( x ) d x C ( ʃ 0 | f ( x ) | p v ( x ) d x ) ( q 0 + + q n ) / p . Such inequalities can always be simplified to nth-order reduced inequalities, where the exponent q 0 = 0 . When n = 1, the reduced inequality is a standard weighted norm inequality, and characterizing the weights is easy. We also find necessary and sufficient conditions on the weights for second-order reduced Opial inequalities to hold. ...