论文信息 - Inverse Volume Inequalities for Matrix Weights

Inverse Volume Inequalities for Matrix Weights

For weights in the matricial Muckenhoupt classes we investigate a number of properties analogous to properties which hold in the scalar Muckenhoupt classes. In contrast to the scalar case we exhibit for eachp ,1 <p<1, a matrix weight W 2Ap;qn S p0<pAp0;q0. We also give a necessary and suYcient condition on W inAp;q, a "reverse inverse volume inequality", to ensure thatW is inAp0;q0 for somep 0 <p .

Marcin Bownik | Marcin Bownik

[1] A. Volberg,et al. MATRIX Ap WEIGHTS VIA S-FUNCTIONS , 1997 .

[2] Sergei Treil,et al. Wavelets and the Angle between Past and Future , 1997 .

[3] S. Bloom. Pointwise multipliers of weighted BMO spaces , 1989 .

[4] B. Muckenhoupt,et al. Weighted norm inequalities for the Hardy maximal function , 1972 .

[5] Alexander Volberg,et al. Matrix _{} weights via -functions , 1997 .

[6] Nicolas Bourbaki,et al. Eléments de Mathématique , 1964 .

[7] N. Tomczak-Jaegermann. Banach-Mazur distances and finite-dimensional operator ideals , 1989 .

[8] S. Treil,et al. Continuous frame decomposition and a vector Hunt-Muckenhoupt-Wheeden theorem , 1997 .

[9] Timothy S. Murphy,et al. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals , 1993 .

[10] B. Bollobás. THE VOLUME OF CONVEX BODIES AND BANACH SPACE GEOMETRY (Cambridge Tracts in Mathematics 94) , 1991 .

[11] R. A. Hunt,et al. Weighted norm inequalities for the conjugate function and Hilbert transform , 1973 .

[12] G. Pisier. The volume of convex bodies and Banach space geometry , 1989 .

[13] A. Calderón,et al. Cauchy integrals on Lipschitz curves and related operators. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[14] Ronald R. Coifman,et al. Weighted norm inequalities for maximal functions and singular integrals , 1974 .