THE SOLUTION OF SOME INTEGRAL EQUATIONS WITH THE LEGENDRE 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 Legendre function in the kernels are considered. Using the representations of the integral operators in the left – hand sides of the considering equations as the compositions of fractional integral operators with power weights, the conditions for their boundedness from one weight spaces of summable functions into other spaces were established earlier. These results are applied to deduce explicit solutions of the integral equations in considered spaces, studied in the paper.
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References
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