We study Besov spaces 5°(LP(I2)), 0<p,q,a<oo,on do- mains I2 in Rd . We show that there is an extension operator W which is a bounded mapping from B°(LP(U.)) onto B%(Lp(Rd)). This is then used to derive various properties of the Besov spaces such as interpolation theorems for a pair of B%(Lp(il)), atomic decompositions for the elements of 5°(Lp(f2)), and a description of the Besov spaces by means of spline approximation.
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DeVore et al. (1993) studied this question.