We show that in the one-dimensional case the weighted Hardy–Littlewood maximal operator Mμ is bounded on BMO(μ) for arbitrary Radon measure μ, and that this is not the case in higher dimensions.

In this paper, we establish several different characterizations of the vanishing mean oscillation space associated with Neumann Laplacian $$\Delta _N$$ , written $${\text {VMO}}_{\Delta _N}({\mathbb {R}^n})$$ . We first describe it classical {VMO}}({\mathbb and certain {VMO}}$$ on half-spaces. Then demonstrate that is actually {BMO}}_{\Delta -closure smooth functions compact supports. Beyond th...

We show that the minimal discrepancy of a point set in d-dimensional unit cube with respect to BMO seminorm suffers from curse dimensionality.

Sentetik boyaların varlığından kaynaklanan su kirliliği, dünyanın en önemli çevresel sorunlarından biridir. Remazol Brilliant Blue R (RBBR), tekstil endüstrisi atıksularından salınan ve suda ciddi kirliliğe neden olan oldukça toksik boyalardan Bu çalışmada, Pseudomonas putida ile üretilmiş biyojenik mangan oksit (BMO) RBBR’ nin giderimi incelenmiştir. BMO giderimi, çeşitli çözelti pH’ ı, dozajı...

In this paper we prove sharp weighted BMO estimates for singular integrals, and show how such can be extrapolated to Banach function spaces.

We find the best possible constant C in inequality‖φ‖Lrpr⩽C‖φ‖Lppr‖φ‖BMO1−pr for all values of parameters p and r such that 1⩽p<r<+∞. To solve problem, we define explicitly compute corresponding Bellman function. This function depends on three variables has a rather complicated structure. first problem an interval then transfer our results to circle line. also obtain explicit estimates several ...