On the Fourier transform of
On the Fourier transform of the symmetric decreasing rearrangements
Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the behavior of a Fourier transform of a function over a small set is controlled by the behavior of the Fourier transform of its symmetric decreasing rearrangement. In the case, the same is true if we further assume that the function has a support of finite measure.As a byproduct, we also give...
On the Fourier Transformation of Positive, Positive Definite Measure on Commutative Hypergroups, and Dual Convolution Structures.
On the Fourier-Laplace representation of analytic functions in tube domains.
On The Frequency With Which Bounded Functions Have Spectral Gaps
On the function of Marcinkiewicz
On the generalization of the Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized to the ergodic Hilbert transform.
On the generalized Fourier transforms associated with Schrödinger operators with long-range perturbations.
On the generalized Hardy's inequality of McGhee, Pigno and Smith and the problem of interpolation between BMO and a Besov space.
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.