Applied Mathematics & Information Sciences

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In this article, we establish conditions on continuous restrictively bounded linear mapping T from S to S′ associated with the kernel K under which the operator T extends to a bounded operator T : Lp 􏰀Rl􏰁 → Lp 􏰀Rl􏰁. Next, we generalize the interpolation theorem for new functional classes, we show that bounded operator T defined, whose kernel satisfies the standard conditions, is bounded with respect to convex seminorm, so, an inequality M ̃ 1 −1 􏰈􏰄M ̃ 1 (|T ( f )|)􏰅μ 􏰉 ≤ A1 M ̃ 1 −1 􏰈􏰄M ̃ 1 (| f |)􏰅μ 􏰉 holds for the constant A1 that depends only on A, M1, M2.

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