Hardy inequality in block weighted spaces
In this study, we prove the classical Hardy inequality in block weighted sequence space. Also, by a non-negative function K = K (x, y) we define corresponding continuous case of the block sequence space. Indeed, by a non-negative Lebesgue measurable function K on (0, infinity) x (0, infinity), we define L-K(p) := {f : integral(infinity)(0)(integral(infinity)(0) K(x, y)vertical bar f(x)vertical bar dx)(p)dy < infinity}. The space L-K(p) equipped by the norm parallel to f parallel to(p,K) = (integral(infinity)(0) (integral(infinity)(0) K(x, y)vertical bar f(x)vertical bar dx)(p)dy)(1/p) is a normed linear space. Finally, for K which is homogeneous of degree theta we prove that parallel to f parallel to(p,K) <= C(p, q, theta) (integral(infinity)(0) x(p(1+theta))vertical bar f(p)(x)vertical bar dx)(1/p).
block weighted sequence space integral inequality hardy's inequality nurlond's operator