Geodesic
Error estimates of cubature formulas exact for Haar polynomials in classes of two-variable functions satisfying a general Lipschitz condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1985-1996

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Upper error estimates are obtained for cubature formulas with the Haar $d$-property in the classes $\mathrm{Lip}(L_1,L_2)$ of two-variable functions satisfying a general Lipschitz condition. It is shown that the error of minimal cubature formulas possessing the Haar $d$-property have the best order of convergence to zero in the indicated classes. 
@article{ZVMMF_2013_53_12_a3,
     author = {K. A. Kirillov},
     title = {Error estimates of cubature formulas exact for {Haar} polynomials in classes of two-variable functions satisfying a general {Lipschitz} condition},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1985--1996},
     publisher = {mathdoc},
     volume = {53},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a3/}
}
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K. A. Kirillov. Error estimates of cubature formulas exact for Haar polynomials in classes of two-variable functions satisfying a general Lipschitz condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1985-1996. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a3/