THE SOLUTION OF INTEGRAL EQUATIONS WITH THE GAUSS HYPERGEOMETRIC FUNCTION IN KERNELS IN Lv,r - SPACES
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Abstract
Four integral equations of the first kind on the positive half axis involving the Gauss hypergeometric function in the kernels are studied. Using the representations of the integral operators in the left – hand sides of considering equations as compositions of fractional integral operators with power weights, the conditions for their boundedness from one weight spaces of summable functions into another spaces are proved. These results are applied to deduce explicit solutions of studied integral equations in considered spaces.
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References
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