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ONEDIMENSIONAL FORMS OF POISSON TRANSFORMS AND CONJUGATE
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applying Fubini's theorem applying Holder's inequality applying Minkowski's integral bounded linear operator change of variable CONJUGATE OPERATORS convergence theorem Appendix defined in terms Definition derived by applying derived by letting derived by multiplying derived by substituting dt dy E C Titchmarsh f in LP(R f(t+x finite constant follows by applying fractional integrals Fubini's theorem Appendix G 0 OKIKIOLU Henoe Hilbert operator Hilbert transform Holder's inequality Appendix inequality Appendix 8.7 infinitesimal integral expressions integral inequality Appendix integrating with respect inversion formula justified kernels Lebesgue convergence theorem Lebesgue measurable Let f Let the operator Lp-estimates LP(Rn measurable function Minkowski's inequality Appendix Minkowski's integral inequality OKIKIOLU CHAPTER operator H operators defined P0I330N OPERATORS Poisson and Conjugate POISSON OPERATORS positive integer product formula Product Identities representation results involving results of Appendix Riesz semi-group identities substituting xt Suppose theorem Appendix 8.3 variable by substituting Young's inequality Appendix