@article{article_1318033, title={On approximation of functions, conjugate to the functions of several variables belonging to weighted Lipschitz and Zygmund classes}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={53}, pages={1497–1514}, year={2024}, DOI={10.15672/hujms.1318033}, author={Srivastava, Shailesh Kumar and Devaiya, Sachin}, keywords={Degree (error) of approximation, weighted Lipschitz class, weighted Zygmund class, N-multiple matrix means}, abstract={In the present paper, we introduce a new weighted Lipschitz class $W(L^p(T^N),\xi_1(s_1),\dots,\xi_N(s_N))$ and Zygmund class $Z(L^p(T^N),\xi_1(s_1),\dots,\xi_N(s_N))$ for $N\in\mathbb{N}$, which generalizes the classes given in [12, 16]. We prove two theorems about the degree (error) of approximation of functions, conjugate to the $N$-variable functions ($2\pi$-periodic in each variable) belonging to these classes using the $N$-multiple matrix means of their $N$-multiple conjugate Fourier series. We improve the results of Móricz and Rhoades [11] and M\’{o}ricz and Shi [12], which are given in the form of corollaries.}, number={6}, publisher={Hacettepe University}