On the generalized Hardy's inequality of McGhee, Pigno and Smith and the problem of interpolation between BMO and a Besov space.
On the Hausdorff summability of series associated with a Fourier and its allied series
Recently, Tripathy - Jour. Ind. Math. Soc., 32 (1960), 141-154 - has proved some results on absolute Hausdorff summability of some series associated with Fourier series and its allied series, which generalise the results proved by Mohanty on absolute Cesaro summability. Proceeding on the similar lines, the author has generalised the results of Cheng - Duke Math. Jour., 15 (1948), 17-27 - by proving them on absolute Hausdorff summability.
On the Heisenberg-Pauli-Weyl inequality.
On the Heisenberg-Weyl inequality.
On the hypercontractivity property.
On the integrability and L¹-convergence of double trigonometric series
On the integrability and L¹-convergence of sine series
On the integrability of a class of integral transforms
On the integrability of Walsh-Fourier transform.
On The Interpolation Between Certain Theorems On Fourier Transforms.
On the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm
Boulahia and the present authors introduced the Orlicz norm in the class -a.p. of Besicovitch-Orlicz almost periodic functions and gave several formulas for it; they also characterized the reflexivity of this space [Comment. Math. Univ. Carolin. 43 (2002)]. In the present paper, we consider the problem of k-convexity of -a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.
On the -convergence of Fourier series
Since the trigonometric Fourier series of an integrable function does not necessarily converge to the function in the mean, several additional conditions have been devised to guarantee the convergence. For instance, sufficient conditions can be constructed by using the Fourier coefficients or the integral modulus of the corresponding function. In this paper we give a Hardy-Karamata type Tauberian condition on the Fourier coefficients and prove that it implies the convergence of the Fourier series...
On the norm of exponential sums
The norm of a trigonometric polynomial with non zero coefficients of absolute value not less than 1 exceeds a fixed positive multiple of
On the local properties of factored Fourier series.
On the local properties of factored Fourier series.
On the localization of factored Fourier series.
On the localization property of square partial sums for multiple Fourier series
On the maximal Fejér operator for double Fourier series of functions in Hardy spaces
We consider the Fejér (or first arithmetic) means of double Fourier series of functions belonging to one of the Hardy spaces , , or . We prove that the maximal Fejér operator is bounded from or into weak-, and also bounded from into . These results extend those by Jessen, Marcinkiewicz, and Zygmund, which involve the function spaces , , and with 0 < μ < 1, respectively. We establish analogous results for the maximal conjugate Fejér operators. On closing, we formulate two conjectures....
On the mean summability by Cesàro method of Fourier trigonometric series in two-weighted setting.
On the method of approximation by families of linear polynomial operators.