Characterizations of the BMO and Lipschitz Spaces via Commutators on Weak Lebesgue and Morrey Spaces

Generalised Gagliardo–Nirenberg inequalities using weak Lebesgue spaces and BMO

Using elementary arguments based on the Fourier transform we prove that for 1 ≤ q < p < ∞ and s ≥ 0 with s > n(1/2 − 1/p), if f ∈ L(R) ∩ Ḣ(R) then f ∈ L(R) and there exists a constant cp,q,s such that ‖f‖Lp ≤ cp,q,s‖f‖ θ Lq,∞‖f‖ 1−θ Ḣs , where 1/p = θ/q+(1− θ)(1/2− s/n). In particular, in R we obtain the generalised Ladyzhenskaya inequality ‖f‖L4 ≤ c‖f‖ 1/2 L2,∞ ‖f‖ 1/2 Ḣ1 . We also show that f...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

On isomorphism of two bases in Morrey-Lebesgue type spaces

Double system of exponents with complex-valued coefficients is considered. Under some conditions on the coefficients, we prove that if this system forms a basis for the Morrey-Lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.

Weighted estimates of higher order commutators generated by BMO-functions and the fractional integral operator on Morrey spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...