Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
In this short report we estimate and calculate the exact value of norms of multilinear integral operators having homogeneous kernel, acting between two Grand Lebesgue Spaces.
This paper contains 2 sections, 1 theorem, 28 equations.
Theorem 2.1
Let $\ G\psi_j(a_j, b_j), \ j = 1,2,\ldots,m$, where $\ 1 \le a_j < b_j \le \infty$, be Grand Lebesgue Spaces with generating functions $\ \psi_j(\cdot)$ and put $\vec{\psi}=(\psi_1,\ldots,\psi_m)$. Let $\beta_m[Q, \vec{\psi}](p)$ defined by where $\Theta_m(\vec{p})$ is defined in key value and the kernel $Q$ is homogeneous of degree $-m$. Then, the multilinear integral operator defined in multil
