Description of the Range of Potentials, and Hypersingular Integrals
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In this chapter we give a complete characterization of the range I α [L p (.)(ℝ n )] in terms of the convergence of hypersingular integrals of order α. The proof is based, in particular, on the results on denseness in L p (.)(ℝ n ) of Schwartz functions orthogonal to polynomials, and the inversion of the Riesz potential operator by means of hypersingular integrals.
KeywordsFractional Derivative Convolution Operator Fourier Multiplier Variable Exponent Lizorkin Space
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