Let dγ(x) ≡ πe 2 dx for all x ∈ R be the Gauss measure on R. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators. To this end, the authors first prove that such a local fractional integral operator of order β is bounded from L(γ) to L(γ), or from the...

Existence and uniqueness of mild and classical solutions are discussed for an abstract second-order evolution problem. The nonlinearity contains a local term and a non-local term. The non-local term is an integral in the form of a convolution of a singular kernel and a regular function involving fractional derivatives. This term may be regarded also as a fractional integral of that regular func...

In this paper, the nonlinear system of local fractional partial differential equations is solved via Elzaki transform decomposition method. The method combines a and Adomian Applications related to are presented.

Background—To assess the reliability of pediatric echocardiographic measurements, we compared local measurements with those made at a central facility. Methods and Results—The comparison was based on the first echocardiographic recording obtained on 735 children of HIV-infected mothers at 10 clinical sites focusing on measurements of left ventricular (LV) dimension, wall thicknesses, and fracti...

BACKGROUND To assess the reliability of pediatric echocardiographic measurements, we compared local measurements with those made at a central facility. METHODS AND RESULTS The comparison was based on the first echocardiographic recording obtained on 735 children of HIV-infected mothers at 10 clinical sites focusing on measurements of left ventricular (LV) dimension, wall thicknesses, and frac...

Background—To assess the reliability of pediatric echocardiographic measurements, we compared local measurements with those made at a central facility. Methods and Results—The comparison was based on the first echocardiographic recording obtained on 735 children of HIV-infected mothers at 10 clinical sites focusing on measurements of left ventricular (LV) dimension, wall thicknesses, and fracti...

Weierstrass's everywhere continuous but nowhere diierentiable function is shown to be locally continuously fractionally diierentiable everywhere for all orders below thècritical order' 2?s and not so for orders between 2?s and 1, where s, 1 < s < 2, is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local...

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the "critical order" 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local ...

We establish properties of strong local nondeterminism for several classes of α-stable random fields such as harmonizable-type fractional stable fields with stationary increments, harmonizable and linear fractional stable sheets. We apply these properties to study existence and joint continuity of the local times of stable random fields. Mathematics Subject Classification (2000). 60G52; 60G17; ...