| Summary: | The following generalization of Hardy's inequality is due to I. Klemes (6) (1993); === "There is a constant $c>0$ such that for any function $f in L sb1$(T), === eqalign{ sum sbsp{j=1}{ infty} left(4 sp{-j} sum sb{4 sp{j-1} le n<4 sp{j}} vert f(n) vert sp2 right) sp{1/2} le c Vert f Vert sb1+c sum sbsp{j=1}{ infty} cr qquad qquad qquad left(4 sp{-j} sum sb{4 sp{j-1} le n<4 sp{j}} vert f(-n) vert sp2 right) sp{1/2}.'' cr} === The proof was based on an elegant construction, (L. Pigno and B. Smith (11)), of a certain bounded function whose Fourier coefficients have desired properties. === The chief object of this thesis is to record another proof of the above result by using the construction that was originally used to prove the Littlewood conjecture (8). In addition, a proof is given that the same generalization is equivalent to another one involving the norm of the Besov space $B sbsp{21}{-1/2}.$
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