On summability of a factored Fourier series
P. L. Sharma, R. K. Jain (1970)
Matematički Vesnik
Similarity:
P. L. Sharma, R. K. Jain (1970)
Matematički Vesnik
Similarity:
R. K. Jain, A. Ganguly (1978)
Matematički Vesnik
Similarity:
B. Martić (1964)
Matematički Vesnik
Similarity:
L. Jeśmanowicz (1962)
Annales Polonici Mathematici
Similarity:
A. Nihal Tuncer (2002)
Annales Polonici Mathematici
Similarity:
Using δ-quasi-monotone and any almost increasing sequences we prove a theorem on summability factors of infinite series, which generalizes a theorem of Mazhar [7] on summability factors.
Cihan Orhan (1998)
Czechoslovak Mathematical Journal
Similarity:
In this paper, we give necessary and sufficient conditions on for , , to be translative. So we extend the known results of Al-Madi [1] and Cesco to the case .
V. Swaminathan (1979)
Matematički Vesnik
Similarity:
B. P. Mishra, D. Singh (1976)
Matematički Vesnik
Similarity:
Masafumi Yoshino (2012)
Banach Center Publications
Similarity:
This article studies the summability of first integrals of a -non-integrable resonant Hamiltonian system. The first integrals are expressed in terms of formal exponential transseries and their Borel sums. Smooth Liouville integrability and a relation to the Birkhoff transformation are discussed from the point of view of the summability.
István Blahota, Lars-Erik Persson, Giorgi Tephnadze (2015)
Czechoslovak Mathematical Journal
Similarity:
We prove and discuss some new -type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients . These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of...
Ferenc Móricz (2013)
Studia Mathematica
Similarity:
Let s: [1,∞) → ℂ be a locally Lebesgue integrable function. We say that s is summable (L,1) if there exists some A ∈ ℂ such that , where . (*) It is clear that if the ordinary limit s(t) → A exists, then also τ(t) → A as t → ∞. We present sufficient conditions, which are also necessary, in order that the converse implication hold true. As corollaries, we obtain so-called Tauberian theorems which are analogous to those known in the case of summability (C,1). For example, if the function...
Ferenc Weisz (2009)
Studia Mathematica
Similarity:
It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space to . This implies the almost everywhere convergence of the Fejér means in a cone for all , which is larger than .
Włodzimierz Łenski, Bogdan Roszak (2008)
Banach Center Publications
Similarity:
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.
Włodzimierz Łenski, Bogdan Szal (2011)
Banach Center Publications
Similarity:
We show the general and precise conditions on the functions and modulus of continuity as well as on the entries of matrices generating the summability means and give the rates of approximation of functions from the generalized integral Lipschitz classes by double matrix means of their Fourier series. Consequently, we give some results on norm approximation. Thus we essentially extend and improve our earlier results [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] and the result of...
Victor Klee (1969)
Studia Mathematica
Similarity:
Victor D. Didenko, Anatolii A. Korenovskyi (2011)
Studia Mathematica
Similarity:
Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means , x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.
Ryszard Jajte (2007)
Studia Mathematica
Similarity:
We distinguish a class of unbounded operators in , r ≥ 1, related to the self-adjoint operators in ². For these operators we prove a kind of individual ergodic theorem, replacing the classical Cesàro averages by Borel summability. The result is equivalent to a version of Gaposhkin’s criterion for the a.e. convergence of operators. In the proof, the theory of martingales and interpolation in -spaces are applied.
Bjorn Gabriel Walther (2002)
Colloquium Mathematicae
Similarity:
We consider the maximal function where and 0 < a < 1. We prove the global estimate , s > a/4, with C independent of f. This is known to be almost sharp with respect to the Sobolev regularity s.