myn m+n s-(-)" (3x)" 5. (14 points) Show that for any non-negative sequences (In) n=1 and (yn)n=1, one has 1/2 1/2 m=ln=1 This inequality is actually strict if the right hand side of the inequality is finite and strictly positive, but you are not required to prove this; also, you may assume that the right hand side is finite to begin with, for otherwise the inequality is obvious. (Hint: Write I'm yn I'm m+n m+n m+n na ma 2 for some suitable value of a, and apply Cauchy-Schwarz. It may help to evaluate the integral po 1 dt +1 at some point.) 0 myn m+n s-(-)" (3x)" 5. (14 points) Show that for any non-negative sequences (In) n=1 and (yn)n=1, one has 1/2 1/2 m=ln=1 This inequality is actually strict if the right hand side of the inequality is finite and strictly positive, but you are not required to prove this; also, you may assume that the right hand side is finite to begin with, for otherwise the inequality is obvious. (Hint: Write I'm yn I'm m+n m+n m+n na ma 2 for some suitable value of a, and apply Cauchy-Schwarz. It may help to evaluate the integral po 1 dt +1 at some point.) 0