The Kolmogorov–Riesz theorem and some compactness criterions of bounded subsets in weighted variable exponent amalgam and Sobolev spaces

Aydın, İsmail; Ünal, Cihan

doi:10.1007/s13348-019-00262-5

Cited by 15 publications

(5 citation statements)

References 28 publications

(43 reference statements)

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“…This theorem has several extensions to different function spaces with standard translation, see e.g. [7], [15], [25], [26], [40], [29] and with Bessel and Laguerre translations, see [30]. In all but one of our examples the translation is not symmetric.…”

Section: Regularity With Respect To Compactnessmentioning

confidence: 79%

Heat-diffusion semigroup and other translations

Horváth¹

2022

Preprint

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We introduce general translations as solutions to Cauchy or Dirichlet problems. This point of view allows us to handle the heat-diffusion semigroup as a translation. With the given examples Kolmogorov-Riesz characterization of compact sets in certain L p µ spaces are given. Pego-type characterizations are also derived. Finally for some examples the equivalence of the corresponding modulus of smoothness and K-functional is pointed out.

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Section: Regularity With Respect To Compactnessmentioning

confidence: 79%

Heat-diffusion semigroup and other translations

Horváth¹

2022

Preprint

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“…; l q by Theorem 2.1 in [34]. ii) Also, if we follow Theorem 3.8 in [34], Theorem 2.3 in [9], Theorem 5.11 in [10], and Theorem 8 in [1], then we have that…”

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confidence: 90%

Inverse continuous wavelet transform in weighted variable exponent amalgam spaces

Kulak¹,

Aydın²

2020

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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The wavelet transform is an useful mathematical tool. It is a mapping of a time signal to the timescale joint representation. The wavelet transform is generated from a wavelet function by dilation and translation. This wavelet function satis…es an admissible condition so that the original signal can be reconstructed by the inverse wavelet transform. In this study, we …rstly give some basic properties of the weighted variable exponent amalgam spaces. Then we investigate the convergence of the means of f in these spaces under some conditions. Finally, using these results the convergence of the inverse continuous wavelet transform is considered in these spaces.

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“…The space ( ) ( ) is a reflexive Banach space with respect to ‖ ‖ ( ) . Moreover, the dual space of ( ) ( ) is isometrically isomorphic to ( ) ( ), where ( ) ( ) and ( ) (see [18][19][20]). The relations between the modular ( ) ( ) and ‖ ‖ ( ) are given in the following theorem (see [19,[21][22]).…”

Section: Theorem 3 Let ( ) ( )mentioning

confidence: 99%

Weighted Variable Exponent Lebesgue Spaces on a Probability Space

AYDIN,

AYDIN

2023

J. Sci. Arts

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In this paper, we introduce the weighted variable exponent Lebesgue spaces defined on a probability space and give some information about the martingale theory of these spaces. We first prove several basic inequalities for expectation operators and obtain several norm convergence conditions for martingales in weighted variable exponent Lebesgue spaces. We discuss the Hölder inequality and embedding properties in these spaces. Finally, under some conditions we investigate Doob’s maximal function.

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The Kolmogorov–Riesz theorem and some compactness criterions of bounded subsets in weighted variable exponent amalgam and Sobolev spaces

Abstract: We study totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces. Moreover, this paper includes several detailed generalized results of some compactness criterions in these spaces.2000 Mathematics Subject Classification. Primary 46E35, 43A15, 46E30.

Cited by 15 publications

References 28 publications

Heat-diffusion semigroup and other translations

Heat-diffusion semigroup and other translations

Inverse continuous wavelet transform in weighted variable exponent amalgam spaces

Weighted Variable Exponent Lebesgue Spaces on a Probability Space

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