Higher integrability results and Hölder continuity

Numerical Interpretation of The Gurov–Reshetnyak Inequality on The Real Axis

“…Let η 1 ∈ (0, 1) be the root of the equation η = ((f α ) I ) 1/α , cf. (3). It is easily seen that this equation is solvable and the root is unique.…”

“…Fix an ε ∈ (0, 2). Set p = p(ε) = p + R (ε) > 1, α = α(ε) = 1/(p(ε) − 1) and define η 1 = η 1 (ε) by (3). According to Theorem 2.1 and Corollary 2.4, one has Table 1 shows some values of the parameters mentioned obtained in numerical experiments, where the columns 6 and 8 contain the maximum points of the function ψ 0 (α, η) for α = 1/(p − 1) and α = −1/p, correspondingly.…”

“…Fix an ε ∈ (0, 2). Set p = p(ε) = p + R (ε) > 1, α = α(ε) = 1/(p(ε) − 1) and define η 1 = η 1 (ε) by (3). According to Theorem 2.1 and Corollary 2.4, one has…”

“…This property lays the foundation for numerous applications of this class of functions. More precisely, for any ε ∈ (0, 2) there are [1], [3], [4], [7], [5], [8], [16], [18]). For R = R + , the exact limiting value…”