The Hp(Zn)-Hq(Zn) boundedness of the discrete Riesz potential

Key Points

• The discrete Riesz potential Iα is a bounded operator between specific function spaces Hp(Zn) and Hq(Zn), now extended to a broader range.
• Previous findings covered a limited parameter range; the new result includes all 0 < p ≤ 1, enhancing its applicability in analysis.
• This research contributes to operator theory by clarifying the conditions under which discrete Riesz potentials maintain boundedness.
• The results have implications for n-dimensional spaces in mathematical analysis, enriching the understanding of function space interactions.