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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/b514473286245w On the Conditions for the Embedding of Classes of Besicovitch Almost Periodic Functions
Khasanov, Yu. Kh.
Vladikavkaz Mathematical Journal 2021. Vol. 23. Issue 1.
Abstract:
In the paper we established some conditions for embedding of classes of \(B_q\)almostperiodic functions into the classes of \(B_p\)almostperiodic in the sense of Besicovitch functions with arbitrary Fourier exponents for \({1\leq p<q<\infty}\). Some of established conditions are counterparts of the known results of other authors on embedding of the classes \(L_p\) \((1\leq p<\infty)\) of periodic functions. As a structural characteristic of such functions we use a higherorder modulus of smoothness with a predetermined step. Since the space of almost periodic Besicovitch functions is a complete normed space, the BochnerFejer polynomials are used as polynomials of best approximation. We also indicate some conditions for the Besicovitch functions to belong to the class of entire functions of bounded degree. It is established that if a \(B_p\)almost periodic \(f(x)\in B_p\) has the best approximation value by entire functions of bounded degree, then there exists the absolutely continuous derivative of the function which is also \(B_p\)almost periodic.
Keywords: Besicovitch almost periodic functions, Fourier series, trigonometric polynomials, embedding theorems, spectral function, modulus of continuity, entire function, BochnerFejer polynomials
Language: Russian
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For citation: Khasanov, Yu. Kh. On the Conditions for the Embedding of Classes of Besicovitch Almost Periodic Functions, Vladikavkaz Math. J., 2021, vol. 23, no. 1, pp. 8898 (in Russian).
DOI 10.46698/b514473286245w ← Contents of issue 
 

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