On a generalization of the concept of derivative
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Publication:4114278
DOI10.1007/BF01896477zbMath0345.42011OpenAlexW2060067436MaRDI QIDQ4114278
No author found.
Publication date: 1977
Published in: Acta Mathematica Academiae Scientiarum Hungaricae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01896477
Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Harmonic analysis on specific compact groups (43A75) Summability methods on groups, semigroups, etc. (43A55)
Related Items (49)
Investigations of certain operators with respect to the Vilenkin system ⋮ On the characterization of the dyadic derivative ⋮ On the convergence of Fejér means of Walsh-Fourier series in the space \(H_p\) ⋮ A sharp boundedness result concerning some maximal operators of Vilenkin-Fejér means ⋮ Sharp \(H_{p}\)-\(L_{p}\) type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications ⋮ On the Nörlund means of Vilenkin-Fourier series ⋮ On the almost everywhere convergence of Fejér means of functions on the group of 2-adic integers ⋮ Convergence of \(T\) means with respect to Vilenkin systems of integrable functions ⋮ Sharp $(H_p,L_p)$ and $(H_p,\text{weak}-L_p)$ type inequalities of weighted maximal operators of $T$ means with respect to Vilenkin systems ⋮ On the pointwise convergence of Cesàro means of two-variable functions with respect to unbounded Vilenkin systems ⋮ \(L^ p\)-norm convergence of series in compact, totally disconnected groups ⋮ The fundamental theorem of two-parameter pointwise derivative on Vilenkin groups ⋮ On the lower bound of Sunouchi's operator with respect to Vilenkin systems ⋮ Fractional modified dyadic integral and derivative on \(\mathbb R_{+}\) ⋮ Some weak type inequalities and almost everywhere convergence of Vilenkin-Nörlund means ⋮ Some new restricted maximal operators of Fejér means of Walsh-Fourier series ⋮ Martingale Hardy spaces and some new weighted maximal operators of Fejér means of Walsh-Fourier series ⋮ Convergence of Vilenkin–Fourier series in variable Hardy spaces ⋮ Almost everywhere convergence of \(T\) means with respect to the Vilenkin system of integrable functions ⋮ Polynomial approximation with respect to multiplicative systems in the Morrey space ⋮ Integrals of weighted maximal logarithmic kernels on bounded Vilenkin groups ⋮ Cesàro means of integrable functions with respect to unbounded Vilenkin systems ⋮ Pointwise strong summability of Vilenkin-Fourier series ⋮ Strong convergence theorems for Walsh-Fejér means ⋮ Pointwise convergence of the Fejér means of functions on unbounded Vilenkin groups ⋮ Unnamed Item ⋮ Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups ⋮ Norm summability of Nörlund logarithmic means on unbounded Vilenkin groups ⋮ On the \((C,\alpha)\)-means with respect to the Walsh system ⋮ Almost everywhere convergence of Banach space-valued Vilenkin-Fourier series ⋮ Pointwise convergence of Marcinkiewicz-Fejér means of double Vilenkin-Fourier series ⋮ Norm convergence of logarithmic means on unbounded Vilenkin groups ⋮ Walsh-Marcinkiewicz means and Hardy spaces ⋮ Almost everywhere convergence of Fejér means of \(L^{1}\) functionson rarely unbounded Vilenkin groups ⋮ Maximal operators of Vilenkin-Nörlund means ⋮ Approximation by Walsh-Marcinkiewicz means on the Hardy space \(H_{2/3}\) ⋮ The derivatives and integrals of fractional order in Walsh-Fourier analysis, with applications to approximation theory ⋮ Strong convergence theorem of Cesàro means with respect to the Walsh system ⋮ Convergence of series of Fourier coefficients for multiplicative convolutions ⋮ Approximation by Vilenkin polynomials in weighted Orlicz spaces ⋮ Some inequalities related to strong convergence of Riesz logarithmic means ⋮ On the boundedness of subsequences of Vilenkin-Fejér means on the martingale Hardy spaces ⋮ Modulus of continuity and convergence of subsequences of Vilenkin-Fejér means in martingale Hardy spaces ⋮ Approximation of functions of bounded \(p\)-fluctuation by polynomials with respect to multiplicative systems ⋮ Vilenkin-Lebesgue points and almost everywhere convergence for some classical summability methods ⋮ On the divergence of Vilenkin-Fourier series ⋮ The \(p\)-adic differential-integral type operator ⋮ Sharp \((H_p, L_p)\) type inequalities of maximal operators of \(T\) means with respect to Vilenkin systems ⋮ Unnamed Item
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