On the generalized absolute convergence of Fourier series
-
Rusudan Meskhia
Abstract
In the present paper the sufficient conditions are obtained for the generalized r-absolute convergence (
References
[1] N. K. Bari, Trigonometric Series (in Russian), Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961. Suche in Google Scholar
[2] Z. A. Chanturia, The moduli of variation of a function and its applications in the theory of Fourier series (in Russian), Dokl. Akad. Nauk SSSR 214 (1974), 63–66; translation in Sov. Math. Dokl. 15 (1974), 67–71. Suche in Google Scholar
[3]
Z. A. Chanturia,
On the absolute convergence of Fourier series of the classes
[4] L. Gogoladze and R. Meskhia, On the absolute convergence of trigonometric Fourier series, Proc. A. Razmadze Math. Inst. 141 (2006), 29–40. Suche in Google Scholar
[5] L. D. Gogoladze, Uniform strong summation of multiple trigonometric Fourier series (in Russian), Reports of the Extended Sessions of a Seminar of the I. N. Vekua Institute of Applied Mathematics. Vol. I, No. 2 (Tbilisi 1985), Tbilis. Gos. Univ., Tbilisi (1985), 48–51, 179. Suche in Google Scholar
[6] T. Karchava, On the absolute convergence of Fourier series, Georgian Math. J. 4 (1997), no. 4, 333–340. 10.1023/A:1022990412102Suche in Google Scholar
[7] F. Móricz and A. Veres, Absolute convergence of multiple Fourier series revisited, Anal. Math. 34 (2008), no. 2, 145–162. 10.1007/s10476-008-0205-7Suche in Google Scholar
[8] P. L. Ul’janov, Series with respect to a Haar system with monotone coefficients (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 925–950. Suche in Google Scholar
[9] A. Zygmund, Remarque Sur la Convergence Absolue des Series de Fourier, J. Lond. Math. Soc. 3 (1928), no. 3, 194–196. 10.1112/jlms/s1-3.3.194Suche in Google Scholar
[10] A. Zygmund, Some points in the theory of trigonometric and power series, Trans. Amer. Math. Soc. 36 (1934), no. 3, 586–617. 10.1090/S0002-9947-1934-1501757-2Suche in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound
- Isomorphism classes of weighted spaces of holomorphic functions on some subsets of complex plane
- Asymptotic behavior of solutions of fractional nabla q-difference equations
- A decomposition theorem for locally compact groups
- An a posteriori truncation regularization method for an ill-posed problem for the heat equation with an integral boundary condition
- Entire function sharing a small function with its mixed-operators
- Hybrid projection method for a system of unrelated generalized mixed variational-like inequality problems
- On the full transitivity of a cotorsion hull
- Comparison results for solutions of elliptic Neumann problems with lower-order terms via Steiner symmetrization
- On the formula of Cohen–Vogt relatively pointed topological semi-simplicial sets
- On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces
- On the generalized absolute convergence of Fourier series
- Embedding theorems for Besov–Morrey spaces of many groups of variables
-
Projective flatness of a new class of
- Spread relation of E-valued meromorphic functions and its application
- q-dual mixed volumes and Lp-intersection bodies
Artikel in diesem Heft
- Frontmatter
- Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound
- Isomorphism classes of weighted spaces of holomorphic functions on some subsets of complex plane
- Asymptotic behavior of solutions of fractional nabla q-difference equations
- A decomposition theorem for locally compact groups
- An a posteriori truncation regularization method for an ill-posed problem for the heat equation with an integral boundary condition
- Entire function sharing a small function with its mixed-operators
- Hybrid projection method for a system of unrelated generalized mixed variational-like inequality problems
- On the full transitivity of a cotorsion hull
- Comparison results for solutions of elliptic Neumann problems with lower-order terms via Steiner symmetrization
- On the formula of Cohen–Vogt relatively pointed topological semi-simplicial sets
- On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces
- On the generalized absolute convergence of Fourier series
- Embedding theorems for Besov–Morrey spaces of many groups of variables
-
Projective flatness of a new class of
- Spread relation of E-valued meromorphic functions and its application
- q-dual mixed volumes and Lp-intersection bodies
