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Order estimates are established for the best bilinear approximations of 2d-variable functions fx−y,x,y∈πd,πd=∏j=1d−ππ$$ f\left(x-y\right),x,y\in {\uppi}_d,{\uppi}_d=\prod {}_{j=1}^d\left[-\uppi, \uppi \right] $$, formed by d-variable functions fx∈Lβ,pψ$$ f(x)\in {L}_{\beta, p}^{\psi } $$by the… Click to show full abstract
Order estimates are established for the best bilinear approximations of 2d-variable functions fx−y,x,y∈πd,πd=∏j=1d−ππ$$ f\left(x-y\right),x,y\in {\uppi}_d,{\uppi}_d=\prod {}_{j=1}^d\left[-\uppi, \uppi \right] $$, formed by d-variable functions fx∈Lβ,pψ$$ f(x)\in {L}_{\beta, p}^{\psi } $$by the shifts of their argument x ∈ πd by all possible values of y ∈ πd in the space Lq1,q2(π2d). The results include various relations between the parameters p, q1, and q2.
Journal Title: Ukrainian Mathematical Journal
Year Published: 2018
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