科研之友
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摘要
We characterize the weights w(0), w(1), w(2) such that the weighted bilinear gradient inequality %26lt;br%26gt;(integral(Rn) vertical bar f(1)(x)f(2)(x)vertical bar(q)w(0)(x)dx)(1/q) %26lt;br%26gt;%26lt;= K (integral(Rn) vertical bar x . del f(1)(x)vertical bar(p1)w(1)(x)dx)(1/p1) (integral(Rn) vertical bar x . del f(2)(x)vertical bar(p2)w(2)(x)dx)(1/p2) %26lt;br%26gt;holds for all functions f(1), f(2) is an element of C-0(infinity) (R-n), with a positive constant K independent of f(1) and f(2), for all possible values of q, p(1) and p(2) with 1 %26lt; q, p(1), p(2) %26lt; infinity.
- 出版日期2014-8
