INTEGRABILITY OF q -BESSEL FOURIER TRANSFORMS WITH GOGOLADZE – MESKHIA TYPE WEIGHTS

Abstract

In the paper, we consider the 𝑞-integrability of functions 𝜆(𝑡)|ℱ𝑞,𝜈 (𝑓)(𝑡)|𝑟, where 𝜆(𝑡) is a Gogoladze-Meskhia-Moricz type weight and ℱ𝑞,𝜈(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 fourier transform
• 𝑞-bessel translation
• weights of gogoladze – meskhia type
• 𝑞-besov space
• modulus of smoothness