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Bloch space

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392: 332: 155: 182: 57: 194: 433: 457: 426: 32: 373: 368: 419: 452: 82: 399: 60: 363: 163: 38: 24: 327:{\displaystyle \|f\|_{\mathcal {B}}=|f(0)|+\sup _{z\in \mathbf {D} }(1-|z|^{2})|f'(z)|.} 403: 446: 185: 20: 70: 391: 67: 16:
Space of holomorphic functions on the open unit disk in the complex plane
210: 169: 128: 44: 407: 197: 166: 85: 41: 326: 176: 149: 51: 245: 341:and the elements of the Bloch space are called 76:in the complex plane, such that the function 427: 8: 205: 198: 150:{\displaystyle (1-|z|^{2})|f^{\prime }(z)|} 434: 420: 316: 294: 285: 280: 271: 255: 248: 236: 219: 209: 208: 196: 168: 167: 165: 142: 127: 118: 109: 104: 95: 84: 43: 42: 40: 354: 7: 388: 386: 31:, named after French mathematician 14: 390: 256: 317: 313: 307: 295: 291: 281: 272: 262: 237: 233: 227: 220: 177:{\displaystyle {\mathcal {B}}} 143: 139: 133: 119: 115: 105: 96: 86: 52:{\displaystyle {\mathcal {B}}} 1: 406:. You can help Knowledge by 458:Mathematical analysis stubs 369:Encyclopedia of Mathematics 337:This is referred to as the 188:, with the norm defined by 474: 385: 362:Wiegerinck, J. (2001) , 402:–related article is a 328: 178: 151: 59:or ℬ, is the space of 53: 400:mathematical analysis 329: 179: 152: 61:holomorphic functions 54: 195: 164: 83: 39: 324: 261: 174: 147: 49: 415: 414: 244: 465: 453:Complex analysis 436: 429: 422: 394: 387: 377: 376: 364:"Bloch function" 359: 333: 331: 330: 325: 320: 306: 298: 290: 289: 284: 275: 260: 259: 240: 223: 215: 214: 213: 183: 181: 180: 175: 173: 172: 156: 154: 153: 148: 146: 132: 131: 122: 114: 113: 108: 99: 58: 56: 55: 50: 48: 47: 25:complex analysis 473: 472: 468: 467: 466: 464: 463: 462: 443: 442: 441: 440: 383: 381: 380: 361: 360: 356: 351: 343:Bloch functions 299: 279: 204: 193: 192: 162: 161: 123: 103: 81: 80: 66:defined on the 37: 36: 17: 12: 11: 5: 471: 469: 461: 460: 455: 445: 444: 439: 438: 431: 424: 416: 413: 412: 395: 379: 378: 353: 352: 350: 347: 335: 334: 323: 319: 315: 312: 309: 305: 302: 297: 293: 288: 283: 278: 274: 270: 267: 264: 258: 254: 251: 247: 243: 239: 235: 232: 229: 226: 222: 218: 212: 207: 203: 200: 171: 158: 157: 145: 141: 138: 135: 130: 126: 121: 117: 112: 107: 102: 98: 94: 91: 88: 46: 15: 13: 10: 9: 6: 4: 3: 2: 470: 459: 456: 454: 451: 450: 448: 437: 432: 430: 425: 423: 418: 417: 411: 409: 405: 401: 396: 393: 389: 384: 375: 371: 370: 365: 358: 355: 348: 346: 344: 340: 321: 310: 303: 300: 286: 276: 268: 265: 252: 249: 241: 230: 224: 216: 201: 191: 190: 189: 187: 184:is a type of 136: 124: 110: 100: 92: 89: 79: 78: 77: 75: 72: 69: 65: 62: 34: 30: 26: 22: 408:expanding it 397: 382: 367: 357: 342: 338: 336: 186:Banach space 160:is bounded. 159: 73: 63: 35:and denoted 28: 21:mathematical 18: 33:AndrĂ© Bloch 29:Bloch space 447:Categories 339:Bloch norm 374:EMS Press 269:− 253:∈ 206:‖ 199:‖ 129:′ 93:− 71:unit disc 23:field of 304:′ 19:In the 27:, the 398:This 349:Notes 404:stub 68:open 246:sup 449:: 372:, 366:, 345:. 435:e 428:t 421:v 410:. 322:. 318:| 314:) 311:z 308:( 301:f 296:| 292:) 287:2 282:| 277:z 273:| 266:1 263:( 257:D 250:z 242:+ 238:| 234:) 231:0 228:( 225:f 221:| 217:= 211:B 202:f 170:B 144:| 140:) 137:z 134:( 125:f 120:| 116:) 111:2 106:| 101:z 97:| 90:1 87:( 74:D 64:f 45:B

Index

mathematical
complex analysis
André Bloch
holomorphic functions
open
unit disc
Banach space
"Bloch function"
Encyclopedia of Mathematics
EMS Press
Stub icon
mathematical analysis
stub
expanding it
v
t
e
Categories
Complex analysis
Mathematical analysis stubs

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