# Browsing by Author "E. D. Nursultanov"

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• (2013-04-30)
• (2013-06-14)
Let F and F -I be the direct and inverse Fourier transforms in R n . A function u is called a Fourier transform multiplicator from the Lorentz function space Lpr(R n) into the Lorentz space Lq~(R n) if the operator T,(f) ...
• (2013-04-30)
• (2013-06-14)
The real interpolation method, which stems from the basic Marcinkiewicz theorem, was introduced by Lions and Peetre [1, 2]. It is described by the functor
• (2013-04-30)
In this paper, interpolation theorems for spaces of functions of several variables are used to generalize and refine H¨ormander’s theorem on the multipliers of the Fourier transform from Lp to Lq and the Hardy–Littlewood–Paley ...
• (2013-06-14)
In this paper, interpolation theorems for spaces of functions of several variables are used to generalize and refine H¨ormander’s theorem on the multipliers of the Fourier transform from Lp to Lq and the Hardy–Littlewood–Paley ...
• (2013-04-30)
• (2013-06-14)
In this paper we prove theorems on multiplicators of Fourier series in Lp, where the conditions depend on a parameter p. An example illustrating the importance of these conditions is constructed.
• (2013-06-14)
In the statements of Lemma 3, Corollary 1, and Theorem 1, the restriction on the parameter p must be of the form; I < p < 2. In fact, this condition must be used for proving Theorem 2 on the basis of the above assertions.
• (2013-04-30)
We consider the real interpolation method and prove that for local Morrey spaces, in the case when they have the same integrability parameter, the interpolation spaces are again local Morrey-type spaces with appropriately ...
• (2013-06-14)
We consider the real interpolation method and prove that for local Morrey spaces, in the case when they have the same integrability parameter, the interpolation spaces are again local Morrey-type spaces with appropriately ...
• (2013-06-14)
Let 1 < p ~ q < c~, and let T n be the n-dimensional torus. We say that a sequence A = {Ak)kez~ of complex numbers is a multiplier of trigonometric Fourier series from Lp(T n) into Lq(T n) if for an arbitrary function f E ...
• (2013-04-30)
• (2012-12-26)
In this paper, multipliers of multiple trigonometric Fourier series are studied; upper and lower estimates for the norm of these multipliers are proved; and the exactness of these estimates is shown on certain classes.
• (2013-04-30)
1. Let 1 ∞ f (t) = √ f (x)e−itx dx, x ∈ R, 2π −∞ be the Fourier transform of a function f ∈ L1(R). Inequalities relating the integral properties of functions and their Fourier transforms are well ...
• (2013-06-14)
Suppose that ω is a nonnegative function on [0,∞]. The generalized Lorentz space Λq(ω,R) is the set of all measurable functions f on R such that
• (2013-06-14)
Let A1 be a Banach space, and let A2 be a functional Banach lattice. We letA = (A1,A2) denote the space of A1-valued measurable functions such that f A1 ∈ A2; this space is equipped with the norm
• (2013-04-30)
1. INTERPOLATION METHOD FOR ANISOTROPIC SPACES Let A1 be a Banach space, and let A2 be a functional Banach lattice. We let A = (A1, A2) denote the space of A1-valued measurable functions such that _f _A1 ∈ A2; this space ...
• (2012-09-20)
• (2013-04-30)
An interpolation theorem for a class of net spaces is proved. In terms of Fourier– Haar coeﬃcients, we obtain a test for a function to belong to the net space Npq(M), where 1 < p < ∞ and M is the set of all closed intervals ...