Geodesic
Extrapolation in Grand Lebesgue Spaces with $A_{\infty}$ Weights
Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 539-551

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Results on extrapolation with $A_{\infty}$ weights in grand Lebesgue spaces are obtained. Generally, these spaces are defined with respect to the product measure $\mu_1\times \dotsb\times \mu_n$ on $X_1\times \dotsb\times X_n$, where $(X_i,d_i,\mu_i)$, $i=1,\dots,n$, are spaces of homogeneous type. As applications of the obtained results, new one-weight estimates with $A_{\infty}$ weights for operators of harmonic analysis are derived.
Keywords: weighted extrapolation, strong maximal operators, multiple integral operators, Calderón–Zygmund operators with product kernels, fractional integrals with product kernels.
Mots-clés : grand Lebesgue spaces 
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     author = {V. M. Kokilashvili and A. N. Meskhi},
     title = {Extrapolation in {Grand} {Lebesgue} {Spaces} with $A_{\infty}$ {Weights}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {539--551},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a4/}
}
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V. M. Kokilashvili; A. N. Meskhi. Extrapolation in Grand Lebesgue Spaces with $A_{\infty}$ Weights. Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 539-551. http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a4/