On the generalized Morrey spaces.
On the global wellposedness of the 3-D Navier–Stokes equations with large initial data
On the Gram-Schmidt orthonormalizatons of subsystems of Schauder systems
In one of the earliest monographs that involve the notion of a Schauder basis, Franklin showed that the Gram-Schmidt orthonormalization of a certain Schauder basis for the Banach space of functions continuous on [0,1] is again a Schauder basis for that space. Subsequently, Ciesielski observed that the Gram-Schmidt orthonormalization of any Schauder system is a Schauder basis not only for C[0,1], but also for each of the spaces , 1 ≤ p < ∞. Although perhaps not probable, the latter result would...
On the - boundedness of some fractional integral operators
Let be real matrices such that for each is invertible and is invertible for . In this paper we study integral operators of the form
On the Hartogs-type series for harmonic functions on Hartogs domains in , m ≥ 2
We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.
On the Hausdorff Dimension of Rademacher Riesz Products.
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 Hermite expansions of functions from the Hardy class
Considering functions f on ℝⁿ for which both f and f̂ are bounded by the Gaussian , 0 < a < 1, we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)-finite functions, thus extending a one-dimensional result of Vemuri.
On the hypercontractivity property.
On the identity of minimal and maximal realizations related to Fourier series operators
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 strong maximal functions corresponding to different frames.
On the integrability of Walsh-Fourier transform.
On The Interpolation Between Certain Theorems On Fourier Transforms.
On the John-Strömberg-Torchinsky Characterizstion of BMO.
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.