Bases of exponents with a piecewise linear phase in generalized weighted Lebesgue space

Najafov, T. I.; Nasibova, Natavan; Mamedova, Z. V.

doi:10.1186/s13660-016-1027-y

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…Bilalov [10,11]. A similar result for the Lebesgue space with a variable summability exponent was obtained in [12], the weighted case of the space was considered in [25,26]. In [27], a sufficient condition for the basicity of the system E λ in Lebesgue spaces with a variable summability exponent is found.…”

Section: Introductionmentioning

confidence: 55%

Basicity of a perturbed system of exponents in rearrangement invariant spaces

2023

Transactions Issue Mathematics

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The paper considers a perturbed system of exponents, where the sequence {λn} is defined by the expression λn = m |Pm (n)|, and Pm (x) = x m + a m−1 x m−1 + ... + a 0 is a polynomial of the m-th degree with real coefficients. The basicity problem of this system in rearrangement invariant space X (−π, π) over the interval (−π, π) is studied. A sufficient condition for the system E λ to be a basis in X (−π, π) is found depending on m, the coefficient a m−1 , and on the Boyd indices α X and β X of the space X (−π, π). Some special cases of the space X (−π, π) are considered.

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Section: Introductionmentioning

confidence: 55%

Basicity of a perturbed system of exponents in rearrangement invariant spaces

2023

Transactions Issue Mathematics

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“…For a Lebesgue space with a variable summability exponent, a similar result was obtained in [8], the weighted case of the space was considered in [19], [20].…”

Section: Introductionmentioning

confidence: 84%

Basicity of a Perturbed System of Exponents in Lebesgue Spaces With a Variable Summability Exponent

Nasibova¹

2022

BMJ

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In this paper a system of exponents 1 is considered, where is some polynomial of degree m, m ∈ N. It is proved that under certain conditions on the exponent p (·) the basicity of this system in a Lebesgue space with a variable summability exponent Lp(·) (−π, π) depends on the coefficient αm−1 and m. Moreover, in the case of basicity, it is isomorphic to the classical system of exponents in Lp(·) (−π, π). Earlier in the case the Riesz basicity of this system in L2 (−π, π) was established by Yu.A.Kazmin

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Bases of exponents with a piecewise linear phase in generalized weighted Lebesgue space

Cited by 2 publications

References 9 publications

Basicity of a perturbed system of exponents in rearrangement invariant spaces

Basicity of a perturbed system of exponents in rearrangement invariant spaces

Basicity of a Perturbed System of Exponents in Lebesgue Spaces With a Variable Summability Exponent

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