论文信息 - Relating smoothness to expressions involving Fourier coefficients or to a Fourier transform

Relating smoothness to expressions involving Fourier coefficients or to a Fourier transform

Coefficients of expansion of a function by trigonometric, algebraic and spherical harmonic orthogonal polynomials are related to the smoothness of that function. Hausdorff-Young type and Hardy-Littlewood type inequalities will be utilized. Expressions involving the Fourier transform of a function are also related to the measure of smoothness of that function.

Zeev Ditzian | Z. Ditzian

[1] Elias M. Stein,et al. Interpolation of linear operators , 1956 .

[2] G. Tolstov. Fourier Series , 1962 .

[3] C. Bennett,et al. Interpolation of operators , 1987 .

[4] Z. Ditzian,et al. Fractional Derivatives and Best Approximation , 1998 .

[5] E. Stein,et al. Introduction to Fourier Analysis on Euclidean Spaces. , 1971 .

[6] Estimates of the coefficients of the Jacobi expansion by measures of smoothness , 2011 .

[7] Feng Dai,et al. Combinations of multivariate averages , 2004, J. Approx. Theory.

[8] Z. Ditzian,et al. Convexity, moduli of smoothness and a Jackson-type inequality , 2011, 1403.3632.

[9] E. Stein,et al. Interpolation of operators with change of measures , 1958 .

[10] L. Grafakos. Classical Fourier Analysis , 2010 .

[11] Z. Ditzian,et al. A modulus of smoothness on the unit sphere , 1999 .

[12] Z. Ditzian. Smoothness of a function and the growth of its Fourier transform or its Fourier coefficients , 2010, J. Approx. Theory.

[13] Z. Ditzian,et al. Equivalence of measures of smoothness in $L_{p}(S^{d-1})$, 1 < p < ∞ , 2010 .