Geodesic
Integrability of $q$-Bessel Fourier transforms with Gogoladze--Meskhia type weights
Problemy analiza, Tome 13 (2024) no. 1, pp. 24-36

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In the paper, we consider the $q$-integrability of functions $\lambda(t)|\mathcal F_{q, \nu}(f)(t)|^r$, where $\lambda(t)$ is a Gogoladze-Meskhia-Moricz type weight and $\mathcal F_{q, \nu}(f)(t)$ is the $q$-Bessel Fourier transforms of a function $f$ from generalized integral Lipschitz classes. There are some corollaries for power type and constant weights, which are analogues of classical results of Titchmarsh et al. Also, a $q$-analogue of the famous Herz theorem is proved.
Keywords: $q$-Bessel translation, modulus of smoothness, weights of Gogoladze–Meskhia type
Mots-clés : $q$-Bessel Fourier transform, $q$-Besov space. 
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     author = {Yu. I. Krotova},
     title = {Integrability of $q${-Bessel} {Fourier} transforms with {Gogoladze--Meskhia} type weights},
     journal = {Problemy analiza},
     pages = {24--36},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2024_13_1_a1/}
}
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Yu. I. Krotova. Integrability of $q$-Bessel Fourier transforms with Gogoladze--Meskhia type weights. Problemy analiza, Tome 13 (2024) no. 1, pp. 24-36. http://geodesic.mathdoc.fr/item/PA_2024_13_1_a1/