Relative rearrangement and Lebesgue spaces L^{p()} with variable exponent
Copyright policy )Relative rearrangement and Lebesgue spaces L^{p()} with variable exponent
We apply the techniques of monotone and relative rearrangements to the non rearrangement invariant spaces Lp(·) (? ) with variable exponent. In particular, we show that the maps u ? L p( ·) (? ) -> k(t )u* ? L p * (·)(0, meas? ) and u ? L p( ·) (? ) -> u* ? Lp* (·) (0, meas? ) are locally ?-Ho?lderian (u * (resp. p* ) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents.
Rearrangement; Variable Lebesgue spaces; Sobolev embedding theorem; Continuity, Rearrangement, Lebesgue spaces with variable exponent, Monotone rearrangement, Sobolev embedding theorem, Relative rearrangement, Variable Lebesgue spaces, Compact Sobolev embedding, Continuity
Rearrangement; Variable Lebesgue spaces; Sobolev embedding theorem; Continuity, Rearrangement, Lebesgue spaces with variable exponent, Monotone rearrangement, Sobolev embedding theorem, Relative rearrangement, Variable Lebesgue spaces, Compact Sobolev embedding, Continuity
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