On the (P) summability of a sequence of Fourier coefficients
On the partial sums of Walsh-Fourier series
We investigate convergence and divergence of specific subsequences of partial sums with respect to the Walsh system on martingale Hardy spaces. By using these results we obtain a relationship of the ratio of convergence of the partial sums of the Walsh series and the modulus of continuity of the martingale. These conditions are in a sense necessary and sufficient.
On the pointwise estimation of Cesàro kernel of negative order with respect to Walsh-Paley system.
On the pointwise multiplication in Besov and Lizorkin-Triebel spaces.
On the pointwise strong approximation by (C,1)(E,1) means
We present an estimate of the (C,1)(E,1)-strong means with mixed powers of the Fourier series of a function as a generalization of the result obtained by M. Yildrim and F. Karakus. Some corollaries on the norm approximation are also given.
On the polyconvolution with the weight function for the Fourier cosine, Fourier sine, and the Kontorovich-Lebedev integral transforms.
On the polynomials orthogonal in the interval with the weight function
On the Product of Functions in BMO and H
The point-wise product of a function of bounded mean oscillation with a function of the Hardy space is not locally integrable in general. However, in view of the duality between and , we are able to give a meaning to the product as a Schwartz distribution. Moreover, this distribution can be written as the sum of an integrable function and a distribution in some adapted Hardy-Orlicz space. When dealing with holomorphic functions in the unit disc, the converse is also valid: every holomorphic...
On the product theory of singular integrals.
We establish Lp-boundedness for a class of product singular integral operators on spaces M = M1 x M2 x . . . x Mn. Each factor space Mi is a smooth manifold on which the basic geometry is given by a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type. The standard singular integrals on Mi are non-isotropic smoothing operators of order zero. The boundedness of the product operators is then a consequence of a natural Littlewood- Paley theory on M. This in...
On the proof of Erdős' inequality
Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality for a constrained polynomial of degree at most , initially claimed by P. Erdős, which is different from the one in the paper of T. Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval and establish a new asymptotically sharp inequality.
On the properties of oscillation and almost periodicity of certain convolutions
On the Pseudodilation Representations of Flornes, Grossman, Holschneider, and Torresani.
On the quantitative Fatou property
The result of this article together with [1] and [4] gives a full quantitative description of a Fatou type property for functions from Hardy classes in the upper half plane.
On the Quotient Function Employed in the Blind Source Separation Problem
MSC 2010: 42C40, 94A12On the blind source separation problem, there is a method to use the quotient function of complex valued time-frequency informations of two ob-served signals. By studying the quotient function, we can estimate the number of sources under some assumptions. In our previous papers, we gave a mathematical formulation which is available for the sources with-out time delay. However, in general, we can not ignore the time delay. In this paper, we will reformulate our basic theorems...
On the Rademacher maximal function
This paper studies a new maximal operator introduced by Hytönen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The -boundedness of this operator depends on the range space; certain requirements on type and cotype are present for instance. The original Euclidean definition of the maximal function is generalized to σ-finite measure spaces with filtrations and the -boundedness is shown not to depend on the underlying measure space or the filtration. Martingale techniques...
On the range of the Fourier transform connected with Riemann-Liouville operator
We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.
On the rate of pointwise summability of Fourier series.
On the rate of strong summability by matrix means in the generalized Hölder metric.
On the rate of strong summability of double Fourier series
Estimates of the strong means of Marcinkiewicz type with the Cesaro means of negative order in one of the variables instead of square partial sums are obtained by characteristics constructed on the basis of moduli of continuity.
On the rate of summability by matrix means in the generalized Hölder metric
We will generalize and improve the results of T. Singh [Publ. Math. Debrecen 40 (1992), 261-271] obtaining the L. Leindler type estimates from [Acta Math. Hungar. 104 (2004), 105-113].