On the (P) summability of a sequence of Fourier coefficients
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 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 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 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 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].
On the refined Heisenberg-Weyl type inequality.
On the regular Sturm-Liouville transform.
On the relation between Gaussian measures and convolution semigroups of local type.
On the representation of functions by trigonometric series
On the strict convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm.
The problem of strict convexity of the Besicovitch-Orlicz space of almost periodic functions is considered here in connection with the Orlicz norm. We give necessary and sufficient conditions in terms of the function f generating the space.
On the strong Cesàro summability of double orthogonal series
On the strong matrix summability of derived Fourier series.
On the strong maximal function and Zygmund’s class
On the strong summability and approximation of Fourier series
On the summability of Fourier series of functions of Λ-bounded variation
On the theorem of Ivasev-Musatov. I
We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.