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Some Integral Inequalities
Application of the Second Method
Application to Harmonic Functions
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analytic apply assume Banach space belong bounded closed compact conclude condition cone consider constant contains continuous converges convex Corollary corresponding defined definition denote depending derivatives determined difference dx dy eigenvalues element equal equation equivalent example exists expression extended fact finite Fourier function given gives harmonic Hence holds identity immediately implies independent inequality infinite integral introduce kernel Lemma linear locally Math matrix means measure method metric necessary norm normal observe obtain operator particular positive potentials present problem proof prove relations Remark replaced require respectively restriction satisfies sequence Similarly singular solution space Subsection subspace sufficient Suppose Theorem theory transformation true University valid values variables verified zero