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APPROXIMATIVE METHOD FOR THE INVERSION OF THE RIESZ POTENTIAL OPERATOR IN VARIABLE LEBESGUE SPACES

We consider the problem of inversion of the Riesz potential operator on variable exponent Lebesgue spaces L p(¢) (R n ). To this end, we extend the so called method of approximative inverses known in the case of constant p, to the case of variable exponents p(x). The main advantage of this approach is the possibility to cover the case when p(x) may take values equal to 1.