[PDF] Top 20 Interpolation in variable exponent spaces

... present interpolation results in these new vari- able exponent ...complex interpolation of variable exponent Lebesgue spaces has been considered in [11, 12, ...Real ... See full document

... Sobolev spaces with variable exponent have been intensively studied during the last ...found. In particular, embeddings of Sobolev spaces started to be investigated since the beginning ... See full document

... Suppose now that W ϕ + H ϕ is invertible (and consequently, W −→ ϕ and W ←− ϕ are also invertible operators). Applying Lemmas 10 and 11, it follows that there exist functions f − = ϕ f o and g − = g o ϕ −1 enjoying the ... See full document

... [50] in the classical case (see also [56] for some correction of the argument) overcoming the diculties caused by the consideration of the general ...see in [32] and [33], where the variable ... See full document

... appear in those wave diffraction problems are considered within a framework of Bessel potential (or Sobolev) spaces; see [7, 8, ...done in the smoothness of the spaces so that the initial ... See full document

... with variable exponent for spatial and spher- ical potential operators, ...α in the weighted Lebesgue generalized spaces L p( ·) ( R n , ρ) with the variable exponent p(x) and a ... See full document

... engaged in the theory of interpolation of Sobolev spaces with such weights, and also with weights of more general type, satisfying certain regularity ...the interpolation theory of weighted ... See full document

... The variable exponent Lebesgue spaces have been intensively investigated in the last ...time in the literature in 1931 due to Orlicz [19] and the growing interest in these ... See full document

... Lebesgue spaces with variable exponent L p( ·) (Ω) have been intensively studied during the last ...operators in the context of the L p( ·) ...these spaces. For details on the recent ... See full document

... (2) in the variable exponent setting was not easy to justify, in particular because the apparatus of the Wiener algebra of Fourier transforms of integrable function, based on the Young ... See full document

... H¨older spaces H λ(·) (X) of functions f on a metric measure space (X, d, μ) , whose H¨older exponent λ(x) is variable, depending on x ∈ X ...of variable order α(x) , from such a ... See full document

... of variable exponent Lebesgue spaces, the Hardy inequal- ity in one variable was first obtained in [15], and later generalized in [7], where the necessary and sufficient ... See full document

... ered in S.G. Samko [25] and L. Diening [6], in [6] there being also treated the case of unbounded domains under the assumption that the maximal operator is ...domains in its natural form was proved ... See full document

... tors in both frameworks of standard and variable exponent Lebesgue spaces are considered in this ...between variable exponent Lebesgue spaces and the invertibility ... See full document

... presented in Theorem 13 is prepared by our estima- tions in Theorem ...is in fact a consequence of Theorem ...First, in Theorem 11, we reformulate Theorem 10 in the form to emphasize ... See full document

... that in most cases the convergence implied in the atomic/molecular decompositions holds in the spaces themselves (see The- orem ...referred in the literature (but see [6] for an ... See full document

... of variable exponent spaces has received a thrust in recent years, due mainly to some applications, for example in the modeling of electro- rheological fluids [4, 3, 37] as well as ... See full document

... limiting exponent q(·) in ...be variable up to ...for variable exponents was con- sidered in [24], where this generalization was obtained with a certain additional restriction on the ... See full document

... Singular operators within the framework of the spaces with variable exponents were studied in [36]. From Theorem 4.8 and Remark 4.6 of [36] and the known results on the boundedness of the maximal ... See full document

... In this paper, we prove theorems on the boundedness of the maximal operator 1 |f y|dμy M f x = sup r>0 μBx, r Bx,r within the frameworks of variable exponent Morrey spaces Lp·,ϕ· X on u[r] ... See full document