Sharp estimates for some iterated operators in Orlicz spaces

ELEONOR HARBOURE; OSCAR SALINAS; BEATRIZ VIVIANI

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS

Rocky Mountain Consortium

Año: 2006 vol. 57 p. 1527 - 1542

0035-7596

In [K] and [HSV] sharp Orlicz estimates for the max- imal and conjugate functions on the one dimensional torus were given. Starting from their results we describe the pairs of growth functions (Ã; ´) such that modular LÃ ! LÁ estimates hold for both, the strong maximal function and the nth-iteration of the Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. both, the strong maximal function and the nth-iteration of the Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. both, the strong maximal function and the nth-iteration of the Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. both, the strong maximal function and the nth-iteration of the Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. both, the strong maximal function and the nth-iteration of the Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Ã; ´) such that modular LÃ ! LÁ estimates hold for both, the strong maximal function and the nth-iteration of the Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators. th-iteration of the Hilbert Transform. We also show that our conditions are sharp. These results are achieved in a setting general enough as to include both operators.