Trigonometric Fourier Series and Their Conjugates

Zhizhiashvili, Levan

doi:10.1007/978-94-009-0283-1

Cited by 84 publications

(36 citation statements)

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“…Note that the estimates obtained in this work depend on sequence of the best approximation E n ( f ) M, ω . Similar problems in different spaces have been investigated by several researchers (see, e.g., [1,2,11,27,42,43,[48][49][50][52][53][54][55][56][57]59,60]). …”

Section: Vallée-poussin Sums In Weighted Orlicz Spaces L M (T ω)mentioning

confidence: 99%

Approximation of functions by de la Vallée-Poussin sums in weighted Orlicz spaces

Jafarov

2016

Arab. J. Math.

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Section: Vallée-poussin Sums In Weighted Orlicz Spaces L M (T ω)mentioning

confidence: 99%

Approximation of functions by de la Vallée-Poussin sums in weighted Orlicz spaces

Jafarov

2016

Arab. J. Math.

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“…By H(w ; C(Tm)) we denote the set of functions f 9 C(T 'n) w A review of results concerning conjugate functions of one and several variables can be found in [5][6][7]. Here we give only the results which are closely related to the property of conjugate functions studied here.…”

Section: Ai(h)f(x) = F(x --F Hli) -F(x) A~(h)f(z) = Ai(h)(ai(h)f(z)) mentioning

confidence: 98%

Multidimensional conjugation operators and deformations of the classesZ(ω (2);C(T m ))

Lekishvili¹

1998

Math Notes

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ABSTRACT. The smoothness of conjugate functions of several variables is studied in terms of the second moduli of smoothness. It is proved that in a sufficiently general case the invariance of the classes considered is violated in just the same way as for classes specified by moduli of continuity.KEY WORDS: conjugation operator, function of several variables, modulus of smoothness, Chebyshev norm.w Let R" , , m > 1 be the m-dimensional Euclidean space of points z = (Zx,.. , xm) with real coordinates. Consider the set M = {1,..., m}. Let B be an arbitrary nonempty subset of M, and let CMB be the complement of B in M. We denote by IB[ the cardinality of B and by zB a point in R" whose coordinates with indices from CMB are necessarily zero.

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“…(see [31]). Certainly, Fourier coefficient functionals a k are continuous from L p ([0, 2π), µ, R) into C due to the integral Hölder inequality:…”

Section: Remarkmentioning

confidence: 99%

Isomorphic Classification of Reflexive Müntz Spaces

Lüdkovsky

2017

Mathematics

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Trigonometric Fourier Series and Their Conjugates

Cited by 84 publications

References 0 publications

Approximation of functions by de la Vallée-Poussin sums in weighted Orlicz spaces

Approximation of functions by de la Vallée-Poussin sums in weighted Orlicz spaces

Multidimensional conjugation operators and deformations of the classesZ(ω (2);C(T m ))

Isomorphic Classification of Reflexive Müntz Spaces

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