מושגי ליבה
Studying discrete analogues of Hardy-type inequalities on lattice graphs reveals sharp constants and optimizers behavior.
תקציר
The thesis delves into discrete functional inequalities on lattice graphs, focusing on Hardy-type and Rearrangement inequalities. The study explores the behavior of sharp constants and optimizers in one-dimensional and higher-dimensional cases. Methods like super-solution and Fourier transform are employed to prove weighted Hardy inequalities for specific values of α and β. The results reveal insights into the fundamental differences between continuous and discrete Hardy inequalities in higher dimensions.
סטטיסטיקה
(2.1) contains a two-parameter family of weighted Hardy inequalities.
(2.7) presents a special case with power weights for specific α values.
(2.8) offers an improvement for α ∈ [1/3, 1) ∪ {0}.