Resumen de Fractional type integral operators of variable order

Pablo Rocha, Marta Urciuolo

• We study the boundedness on the variable Lebesgue spaces of the operators of variable orderTΩf(x)=∫Ω|y−A1x|−α1(y)…m|y−Ax|−αm(y)f(y)dy and UΩf(x)=∫Ω|y−A1x|−α1(x)…m| y−Ax|−αm(x)f(y)dy,where αi:Ω⊂Rn→(0,n) are positive measurable functions, for i=1,…,m (m≥ 2), such that α1(x)+⋯+αm(x)=n−α(x) with 0≤α(x)