Let T be the C∗-algebra generated by the Toeplitz operators {Tφ : φ ∈ L∞(S, dσ)} on the Hardy space H(S) of the unit sphere in C. It is well known that T is contained in the essential commutant of {Tφ : φ ∈ VMO∩L∞(S, dσ)}. We show that the essential commutant of {Tφ : φ ∈ VMO∩L∞(S, dσ)} is strictly larger than T .

Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a) are measurable in both time and one spatial variable, and VMO in the other spatial variables. The coefficient a is measurable in time and VMO in the spatial variables. The unique solvability of equations in the whole space is applied to solving Dirichlet and oblique derivative pr...

We prove that the multiparameter (product) space BMO of functions of bounded mean oscillation can be written as the intersection of finitely many dyadic product BMO spaces, with equivalent norms, generalizing the one-parameter result of T. Mei. We establish the analogous dyadic structure theorems for the space VMO of functions of vanishing mean oscillation, for Ap weights, for reverse-Hölder we...

Six normal cadaver lower limbs were mounted on a specially designed loading apparatus. Wires were used to simulate the five muscle bellies of the quadriceps, the ratio of their tensions having been determined from that of the anatomical cross-sectional areas of the muscles. A three-camera system was used to track the patella during knee movements from flexion to extension. The patellofemoral co...

[Purpose] The purpose of this study was to investigate the activation of the vastus medialis oblique muscle (VMO) and vastus lateralis muscle (VL) during squat exercise with various hip adduction loads using a pressure-biofeedback unit, and to suggest the most effective exercise method. [Subjects] We recruited 15 healthy adult females with no pain in the knee joint and no other orthopedic probl...

Well known results related to the compactness of Hankel operators of one complex variable are extended to little Hankel operators of two complex variables. Critical to these considerations is the result of Ferguson and Lacey [5] characterizing the boundedness of the little Hankel operators in terms of the product BMO of S.-Y. Chang and R. Fefferman [2,3].

In this paper, we study Vanishing Mean Oscillation vector fields on a compact manifold with boundary. Inspired by the work of Brezis and Niremberg, we construct a topological invariant — the index — for such fields, and establish the analogue of Morse’s formula. As a consequence, we characterize the set of boundary data which can be extended to nowhere vanishing VMO vector fields. Finally, we s...

Objective To provide the off -loading knee brace was designed relief for the pain associated with osteoarthritis by reduce loads on the degenerative compartment of the knee. Th is study examined the eff ects of the off -loading knee brace on activation of femoral muscles during squatting, slow and fast walking exercise in healthy young individuals. Method Ten healthy male subjects without a his...

A common rehabilitation strategy for patellofemoral pain syndrome (PFPS), which lacks scientific evidence, includes pulling the patella medially with tape to reduce pain and increase the vastus medialis oblique (VMO) muscle activity. The purpose of this study was to examine the effect of various patellar taping procedures on force production, EMG activity of the VMO and vastus lateralis (VL) mu...

Objective: To investigate the reflex response time (RRT) of the vastus medialis obliquus (VMO), vastus lateralis obliquus (VLO) and vastus lateralis longus (VLL) muscles in clinically healthy individuals and subjects with patellofemoral pain syndrome (PPS). Methods: Twelve clinically health women and twelve women with PPS were evaluated. Electromyography (EMG) records were obtained using active...